F  ROM  -TH  E  -  LI  BRARY-  OF 
•WILLIAM -A  HILLEBRAND 


ELECTRICAL  MACHINE  DESIGN 


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ELECTRICAL  MACHINE 
DESIGN 


THE  DESIGN  AND  SPECIFICATION  OF 
DIRECT  AND  ALTERNATING  CURRENT  MACHINERY 


BY 

ALEXANDER  GRAY,  Whit.  Sch.,  B.  Sc.  (Edin.  and  McGill) 

ELECTRICAL  ENGINEERING,   MCGILL   UNIVERSITY 
MONTREAL,    CANADA 


McGRAW-HILL    BOOK   COMPANY 

239  WEST  39TH  STREET,  NEW  YORK 

6  BOUVERIE  STREET,  LOND.ON,  E.  G. 

1913 


COPYRIGHT,  1913,  BY  THE 
McGRAW-HiLL  BOOK  COMPANY 


1HE. MAPLE. PRESS. YORK. PA 


PREFACE 

The  following  work  was  compiled  as  a  course  of  lectures  on 
Electrical  Machine  Design  delivered  at  McGill  University.  Since 
the  design  of  electrical  machinery  is  as  much  an  art  as  a  science 
no  list  of  formulae  or  collection  of  data  is  sufficient  to  enable  one 
to  become  a  successful  designer.  There  is  a  certain  amount  of 
data,  however,  sifted  from  the  mass  of  material  on  the  subject, 
which  every  designer  finds  convenient  to  compile  for  ready 
reference.  This  work  contains  data  that  the  author  found 
necessary  to  tabulate  during  several  years  of  experience  as  a 
designer  of  electrical  apparatus. 

A  study  of  design  is  of  the  utmost  importance  to  all  students, 
because  only  by  such  a  study  can  a  knowledge  of  the  limitations 
of  machines  be  acquired.  The  machines  discussed  are  those 
which  have  become  more  or  less  standard,  namely,  direct-cur- 
rent generators  and  motors,  alternating  current  generators,  syn- 
chronous motors,  polyphase  induction  motors,  and  transformers; 
other  apparatus  seldom  offers  an  electrical  problem  that  is  not 
discussed  under  one  or  more  of  the  above  headings. 

The  principle  followed  throughout  the  work  is  to  build  up  the 
design  for  the  given  rating  by  the  use  of  a  few  fundamental 
formulae  and  design  constants,  the  meaning  and  limits  of  which 
are  discussed  thoroughly,  and  the  same  procedure  has  been 
followed  for  the  several  pieces  of  apparatus. 

The  author  wishes  to  acknowledge  his  indebtedness  to  Mr. 
B.  A.  Behrend,  under  whom  he  learned  the  first  principles  of 
electrical  design  and  whose  influence  will  be  seen  throughout  the 
work;  to  the  engineers  of  the  Allis-Chalmers-Bullock  Company 
of  Montreal,  Canada,  and  particularly  to  Mr.  Bradley  T.  Mc- 
Cormick,  Mr.  G.  P.  Cole  and  Mr.  H.  F.  Eilers;  to  Mr.  A.  Mc- 
N aught on  of  McGill  University  for  criticism  of  the  arrangement 
of  the  work  and  to  Mr.  A.  M.  S.  Boyd  for  assistance  in  the  proof- 
reading. 

McGiLL  UNIVERSITY, 
September  2,  1912. 


99588 


CONTENTS 

SECTION  I 
DIRECT-CURRENT  MACHINERY 

CHAPTER  I 

PAGE 

MAGNETIC  INDUCTION .1 

Lines  of  Force — Direction  of  an  Electric  Current — Magnetic  Field 
Surrounding  a  Conductor — Magneto  Induction — Direction  of  the 
Generated  E.  M.  F. — Magnetomotive  Force. 

CHAPTER  II 

ARMATURE  WINDING 7 

Gramme  Winding — Re-entrancy — Objections  to  the  Gramme 
Winding — Drum  Winding — E.M.F.  Equation — Multipolar  Ma- 
chines— Equalizer  Connections — Short  Pitch  Windings — Mul- 
tiple Windings — Series  Windings — Lap  and  Wave  Windings — 
Shop  Instructions — Several  Coils  in  a  Slot — Number  of  Slots — 
Odd  Windings. 

CHAPTER  III 

CONSTRUCTION  OF  MACHINES 24 

Armature — Poles — Yoke — Co  mmutator —  B  earings — Slide  Rails — 
Large  Machines. 

CHAPTER  IV 

INSULATION 30 

Materials — Thickness — Heat  and  Vibration — Grounds  and  Short- 
circuits — Slot  Insulation — Puncture  Test — End  Connection  Insula- 
tion— Surface  Leakage — Several  Coils  in  a  Slot — Examples  of 
Armature  and  Field  Coil  Insulation. 

CHAPTER  V 

THE  MAGNETIC  CIRCUIT 42 

Leakage  Factor — Magnetic  Areas — Fringing  Constant — Flux 
Densities — Calculation  of  the  No-load  Saturation  Curve  and  of  the 
Leakage  Factor.  , 

CHAPTER  VI 

ARMATURE  REACTION 54 

Armature  Reaction — Flux  Distribution  in  the  Air  Gap — Armature 
Reaction  when  the  Brushes  are  Shifted — Full  Load  Saturation  • 
Curve — Relative  Strength  of  Field  and  Armature. 

vii 


viii  CONTENTS 

CHAPTER  VII 

PAGE 

DESIGN  OF  THE  MAGNETIC  CIRCUIT      62 

Field  Coil  Heating— Size  of  Field  Wire-^-Length  of  Field  Coils- 
Weight  of  Field  Coils — Design  of  the  Field  System  for  a  Given 
Armature. 

CHAPTER  VIII 

COMMUTATION 72 

Resistance  Commutation — Effect  of  the  Self-induction  of  the  Coils 
— Current  Density  in  the  Brush — Reactance  Voltage — Brush  Con- 
tact Resistance — Energy  at  the  Brush  Contact — Reactance 
•  Voltage  for  Full  Pitch  Multiple,  Short  Pitch  Multiple  and  Series 
Windings. 

CHAPTER  IX 

COMMUTATION  (Continued) 85 

Sparking  Voltage — Minimum  Number  of  Slots  per  Pole — Brush 
Arc — Limits  of  Reactance  Voltage — Limit  of  Armature  Loading — 
Interpole  Machines — Interpole  Dimensions — Flashing  Over. 

CHAPTER  X 

EFFICIENCY  AND  LOSSES    . 97 

Efficiency — Bearing  Friction — Brush  Friction — Windage  Loss — 
Iron  Losses — Armature  Copper  Loss — Field  Copper  Loss — Brush 
Contact  Resistance  Loss. 

CHAPTER  XI 

HEATING 104 

Temperature  Rise — Maximum  Safe  Temperature — Temperature 
Gradient  in  the  Core — Limiting  Values  of  Flux  Density — Heating 
of  Winding — Temperature  Gradient  in  the  Conductors — Commu- 
tator Heating — Application  of  the  Heating  Constants. 

CHAPTER  XII 

PROCEDURE  IN  ARMATURE  DESIGN  . 114 

The  Output  Equation — Relation  Between  Diameter  and  Length  of 
the  Armature — Magnetic  and  Electric  Loading — Formulae  for 
Armature  Design — Examples  of  Armature  Design. 

CHAPTER  XIII 

MOTOR  DESIGN  AND  RATINGS 127 

Procedure  in  Design — Ratings  for  Different  Voltages  and  Speeds — 
Enclosed  Motor — Possible  Ratings  for  a  Given  Armature. 

CHAPTER  XIV 

LIMITATIONS  IN  DESIGN 138 

Reactance  Voltage  and  Average  Voltage  per  Bar — High  Voltage — 


CONTENTS  ix 

PAGE 

Large  Current — Best  Winding  for  Commutation — Limits  of  Out- 
put in  Non-interpole,  Interpole,  and  Turbo  Generators. 

CHAPTER  XV 

DESIGN  OF  INTERPOLE  MACHINES 146 

Preliminary  Design — Design  of  Armature,  Commutator  and  Field 
System — Example. 

CHAPTER  XVI 

SPECIFICATIONS 153 

Example — Points  to  be  Observed — Effect  of  Voltage  and  Speed  on 
Efficiency. 

SECTION  II 
ALTERNATORS  AND  SYNCHRONOUS  MOTORS 

CHAPTER  XVII 

ALTERNATOR  WINDINGS 160 

Fundamental  Diagrams — Y  and  A  Connection — Several  Con- 
ductors per  Slot — Chain,  Double-layer  and  Wave  Windings — 
Several  Circuits  per  Phase. 

CHAPTER  XVIII 

THE  GENERATED  ELECTRO-MOTIVE  FORCE 178, 

Form  Factor — Wave  Form — Harmonics  and  Methods  of  Eliminat- 
ing Them — Y  and  A  Connection — Harmonics  Due  to  Armature 
Slots — Effect  of  the  Number  of  Slots  on  the  Voltage — Rating — 
Effect  of  the  Number  of  Phases  on  the  Rating — General  E.  M.  F. 
Equation. 

CHAPTER  XIX 

CONSTRUCTION  OF  ALTERNATORS 191 

Stator — Poles — Field  Ring. 

CHAPTER  XX 

INSULATION 195 

Definitions— Insulators  in  Series — Air  Films — Thickness  of  Insula- 
tion— Potential  Gradient — Time  of  Application  of  the  Strain* — 
Examples  of  Alternator  Insulation. 

CHAPTER  XXI 

ARMATURE  REACTION 208 

Armature  Fields — Vector  Diagram — Full  Load  Saturation  Curves 
— Synchronous  Reactance — Calculation  of  the  Demagnetizing 
Ampere-turns  per  Pole  and  of  the  Leakage  Reactance — End  Con- 
nection, Slot  and  Tooth  Tip  Reactance — Variation  of  Armature 


x  CONTENTS 

PAGE 

Reactance  and  Armature  Reaction  with  Power  Factor — Full 
Load  Saturation  Curves  at  any  Power  Factor — Regulation — 
Effect  of  Pole  Saturation  on  the  Regulation — Relation  Between 
the  M.  M.  FS.  of  Field  and  Armature — Single  Phase  Machines — 
Comparison  Between  Single  and  Polyphase  Alternators. 

CHAPTER  XXII 

DESIGN  OF  THE  REVOLVING  FIELD  SYSTEM 237 

Field  Excitation — Procedure  in  Design — Calculation  of  the  Satura- 


tion Curves. 


CHAPTER  XXIII 


LOSSES,  EFFICIENCY  AND  HEATING 247 

Bearing  Friction — Brush  Friction — Windage  Loss — Iron  Loss — 
Copper  Loss — Eddy  Current  Losses  in  the  Conductors — Efficiency 
— Heating — Internal  Temperature  of  High  Voltage  Machines. 

CHAPTER  XXIV 

PROCEDURE  IN  DESIGN 255 

The  Output  Equation — Relation  Between  Diameter  and  Length  of 
the  Armature — Effect  of  the  Number  of  Poles  on  this  Relation — 
Variation  of  Armature  Length  with  a  Given  Diameter — Windings 
for  Different  Voltages — Examples  of  Alternator  Design. 

CHAPTER  XXV 

HIGH  SPEED  ALTERNATORS 272 

Alternators  Built  for  an  Overspeed — Turbo  Alternators — Rotor 
Construction  and  Stresses — Diameter  of  Shaft — Critical  Speed — 
Heating  of  Turbo  Alternators — Current  on  an  Instantaneous  Short- 
circuit — Gap  Density — Demagnetizing  Ampere-turns  per  Pole — 
Relation  Between  the  M.  M.  FS.  of  Field  and  Armature — Pro- 
cedure in  the  Design  of  Turbo  Alternators — Limitations  Due  to 
Low  Voltage — Single  Phase  Turbo  Alternators. 

CHAPTER  XXVI 

SPECIAL  PROBLEMS  ON  ALTERNATORS 297 

Flywheel  Design — Design  of  Dampers — Synchronous  Motors  for 
Power  Factor  Correction — Design  of  Synchronous  Motors — Self- 
starting  Synchronous  Motors. 

CHAPTER  XXVII 

ALTERNATOR  SPECIFICATIONS 312 

Example — Notes  on  Alternator  Specifications — Effect  of  Voltage 
and  Speed  on  the  Efficiency. 


CONTENTS  xi 

SECTION  III 
POLYPHASE  INDUCTION  MOTORS 

CHAPTER  XXVIII 

PAGE 

ELEMENTARY  THEORY  OF  OPERATION      319 

Revolving  Field — Multipolar  Motors — Windings — Rotor  Current 
and  Voltage — Starting  Torque — Running  Conditions — Vector 
Diagrams. 

CHAPTER  XXIX 

GRAPHICAL  TREATMENT  OF  THE  INDUCTION  MOTOR 332 

Current  Relations  in  Rotor  and  Stator — Revolving  Fields  of  Rotor 
and  Stator — Flux  Diagram — Proof  of  the  Circle  Law — No  Load 
and  Short-circuit  Points — Representation  of  the  Losses — Relation 
Between  Rotor  Loss  and  Slip — Interpretation  of  the  Circle 
Diagram. 

CHAPTER  XXX 

CONSTRUCTION  OF  THE  CIRCLE  DIAGRAM  FROM  TEST  RESULTS  ....  342 
No  Load  Saturation  Curve — Short-circuit  Curve — Construction  of 
the  Diagram. 

CHAPTER  XXXI 

CONSTRUCTION  OF  INDUCTION  MOTORS 348 

Stator — Rotor. 

CHAPTER  XXXII 

MAGNETIZING  CURRENT  AND  NO-LOAD  LOSSES 352 

E.  M.  F.  Equation — Magnetizing  Current — Friction  Loss — Iron 
Loss — Rotor  Slot  Design — Calculation  of  the  No-load  Losses. 

CHAPTER  XXXIII 

LEAKAGE  REACTANCE 360 

Leakage  Fields — Zig-zag  Reactance — Complete  Formula — Belt 
Leakage — Approximate  Formula  for  Preliminary  Design. 

CHAPTER  XXXIV 

COPPER  LOSSES 371 

Loss  in  the  Conductors — Loss  in  the  End- connectors. 

CHAPTER  XXXV 

HEATING  OF  INDUCTION  MOTORS 375 

Heating  and  Cooling  Curves — Intermittent  Ratings — Heating  at 
Starting — Stator  and  Rotor  Heating — Effect  of  Construction — 
Enclosed  and  Semi-enclosed  Motors. 


xii  CONTENTS 

CHAPTER  XXXVI 

PAGE 

NOISE  AND  DEAD  POINTS  IN  INDUCTION  MOTORS 385 

Windage  Noise — Pulsations  of  the  Main  Field — Vibration  of  the 
Tooth  Tips — Variations  in  the  Leakage  Field — Dead  Points  at 
Starting. 

CHAPTER  XXXVII 

PROCEDURE  IN  DESIGN 391 

The  Output  Equation — Relation  Between  Diameter  and  Length  of 
the  Stator — Preliminary  Design — Detailed  Design — Design  of 
Wound  Rotor  Motors — Variation  of  the  Stator  Length  with  a 
Given  Diameter — Windings  for  Different  Voltages — Examples  of 
Induction  Motor  Design. 

CHAPTER  XXXVIII 

SPECIAL  PROBLEMS  ON  INDUCTION  MOTORS 409 

Slow  Speed  Motors — Closed  Slots — High  Speed  Motors — Two- 
pole  Motors — Effect  of  Variations  in  Voltage  and  Frequency  on 
the  Operation. 

CHAPTER  XXXIX 

INDUCTION  MOTOR  SPECIFICATIONS 422 

Example — Effect  of  Voltage  and  Speed  on  the  Characteristics — 
Specifications  for  Wound  Rotor  Motors. 

SECTION  IV 
TRANSFORMERS 

CHAPTER  XL 

OPERATION  OF  TRANSFORMERS 427 

No-load — Full  Load — Short  Circuit — Regulation. 

CHAPTER  XLI 

CONSTRUCTION  OF  TRANSFORMERS 433 

Small  Core  Type — Large  Shell  Type. 

CHAPTER  XLII 

MAGNETIZING  CURRENT  AND  IRON  Loss      439 

E.  M.  F.  Equation — No-load  Losses — Exciting  Current. 

CHAPTER  XLIII 

LEAKAGE  REACTANCE 445 

Core  Type  with  Two  Coils  per  Leg — Core  Type  with  Split  Secondary 
Windings— Shell  Type. 


CONTENTS  xiii 

CHAPTER  XLIV 

PAGE 

TRANSFORMER  INSULATION 449 

Transformer  Oil — Surface  Leakage — Bushings — Coil  Insulation — 
Extra  Insulation  on  the  End  Turns — Insulation  Between  the 
Windings  and  Core. 

CHAPTER  XLV 

LOSSES,  EFFICIENCY  AND  HEATING 461 

Iron  Loss — Copper  Loss — Eddy  Current  Loss  in  the  Winding — 
Efficiency — Temperature  Gradient  in  the  Oil — Temperature  Gra- 
dient in  Core  and  in  Shell  Type  Transformers — Temperature  of  the 
Oil — Air  Blast  Transformers — Water  Cooled  Transformers — 
Heating  Constants — Effect  of  Oil  Ducts — Maximum  Temperature 
in  the  Windings — Section  of  Wire  in  the  Coils. 

CHAPTER  XL VI 

PROCEDURE  IN  DESIGN 476 

The  Output  Equation — Core  Type  Transformers — Design  of  a 
Distributing  Transformer — Shell  Type  Transformers — Design  of  a 
110, 000- volt  Power  Transformer. 

CHAPTER  XL VII 

SPECIAL  PROBLEMS  IN  TRANSFORMERS 487 

Comparison  Between  Core  and  Shell  Type  Transformers — Three 
Phase  Transformers — Operation  on  Different  Frequencies. 

CHAPTER  XL VIII 

TRANSFORMER  SPECIFICATIONS '.    .    .   494 

Example  for  Distributing  Transformers — Effect  of  Voltage  on  the 
Characteristics. 

CHAPTER  XLIX 

MECHANICAL  DESIGN 499 

Fundamental  Principles — Yokes — Rotors  and  Spiders — Commuta- 
tors— Unbalanced  Magnetic  Pull — Bearings — Shafts — Pulleys — 
Brush  Holders. 

WIRE  TABLE    . 508 

TABLES  OF  SYMBOLS 512 

INDEX   .  .    513 


ELECTRICAL  MACHINE  DESIGN 


CHAPTER  I  \  i:\ji  V 

MAGNETIC  INDUCTIO^  ]  ;•;,  ;     •  i  / '  •  \  ^  ' ; 

1.  Lines  of  Force. — A  magnetic  field  is  represented  by  lines 
of  force.  These  are  continuous  lines  whose  direction  at  any 
point  is  that  of  the  force  acting  on  a  north  pole  placed  at  the 
point,  therefore,  as  shown  in  Fig.l,  lines  of  force  always  leave 
a  north  pole  and  enter  a  south  pole. 


FIG.  1. — Direction  of  lines  of  force. 

2.  Direction  of  an  Electric  Current. — P  and  Q,  Fig.  2,  are  two 
conductors  carrying  current.  The  current  is  going  down  in 
conductor  P  and  coming  up  in  conductor  Q.  If  the  direction  of 


o 


Q 

Up 
FIG.  2. — Direction  of  an  electric  current. 

the  current  be  represented  by  an  arrow,  then  in  conductor  P 
the  tail  of  the  arrow  will  be  seen  and  this  is  represented  by  a 
cross;  in  conductor  Q  the  point  of  the  arrow  will  be  seen  and  this 
is  represented  by  a  point  or  dot. 

1 


2  ELECTRICAL  MACHINE  DESIGN 

3.  Magnetic  Field  Surrounding  a  Conductor  Which  is  Carrying 
Current. — In  conductor  P,  Fig.  3,  an  electric  current  is  passing 
downward.  It  has  been  found  by  experiment  that  in  such  a 
case  the  conductor  is  surrounded  by  a  whirl  of  magnetic  lines  in 
the  direction  shown.  This  direction  can  be  found  by  the  following 
rule:  "If  a  corkscrew  be  screwed  into  the  conductor  in  the 
direction  of  the  current  then  the  head  of  the  corkscrew  will  travel 
in1  the  direction  of; the  lines  of  force." 

'  4.  Magneto'  Induction. — Faraday's  experiments  showed  that 
.when  /the.  magnetic  'flux  threading  a  coil  changes,  an  e.m.f.  is 
generated 'in  tire' coil,  and  that  this  e.m.f.  is  proportional  to  the 
rate  of  change  of  flux  in  the  coil. 


FIG.  3. — Magnetic  field  surrounding  a  conductor. 

The  unit  of  e.m.f.  is  so  chosen  that  one  unit  of  e.m.f.  is  gener- 
ated in  a  coil  of  one  turn  when  the  rate  of  change  of  flux  in  the 
coil  is  one  line  per  second.  This  is  called  the  c.g.s.  unit;  the 
practical  unit,  called  the  volt,  is  108  c.g.s.  units. 

5.  Direction  of  the  Generated  E.M.F. — N  and  S,  Fig.  4,  are 
the  north  and  south  poles  of  a  magnet,  <j>  is  the  total  number 
of  lines  of  force  passing  from  the  north  to  the  south  pole,  A  is  a 
coil  of  one  turn. 

When  the  coil  A  is  moved  from  position  1,  where  the  number 
of  lines  threading  the  coil  is  <f>,  to  position  2,  where  the  number 
of  lines  threading  the  coil  is  zero,  in  a  time  of  t  seconds,  then  the 

average    e.m.f.    generated   in   the  coil   =  ylO~8  volts;  or  at  any 
(  t 

instant  the  e.m.f.  =  -^10~8  volts. 
at 


MAGNETIC  INDUCTION  3 

The  quantity  ~  is  the  rate  at  which  conductor  xy,  Fig.  4,  is 

cutting  lines  of  force,  so  that  the  voltage  generated  by  a  conductor 
which  is  cutting  lines  of  force  is  equal  to 

(the  lines  cut  per  second)  X  10~8. 

The  direction  of  this  e.m.f.  is  found  by  Fleming's  Rule  which 
states  that  "  If  the  thumb,  forefinger  and  middle  finger  of  the 
right  hand  are  all  set  perpendicular  to  one  another  so  as  to 
represent  three  co-ordinates  in  space,  the  thumb  pointed  in  the 
direction  of  motion  of  the  conductor  relative  to  the  magnetic 


FIG.  4. — Direction  of  the  generated  e.m.f. 

field,  and  the  forefinger  in  the  direction  of  the  lines  of  force,  then 
the  middle  finger  will  point  in  the  direction  in  which  the  generated 
e.m.f.  tends  to  send  the  current  of  electiicity." 

The  direction  of  the  e.m.f.  in  Fig.  4  is  found  by  Fleming's  three- 
finger  rule,  and  the  current  due  to  this  e.m.f.  is  in  such  a  direction 
as  to  tend  to  maintain  the  flux  threading  the  coil,  or,  as  stated 
by  the  very  general  law  known  as  Lenz's  Law,  "the  generated 
e.m.f.  always  tends  to  send  a  current  in  such  a  direction  as  to 
oppose  the  change  of  flux  which  produces  it."  The  complete 


4  ELECTRICAL  MACHINE  DESIGN 

statement  of  the  e.m.f.  equation  is,  therefore,  that  the  e.m.f.  at 
any  instant  =  —  -^~10~8  volts. 

6.  Magnetomotive  Force. — In   Fig.    5  the  current  7  passes 
through  the  T  turns  of  the  coil  C  which  is  wound  on  an  iron  core, 
and  a  magnetic  flux  0  is  set  up  in  the  magnetic  circuit.     This 
flux  is  found  to  depend  on  the  number  of  ampere-turns  TI,  and, 
corresponding  to  Ohm's  law  for  the  electric  circuit,  there  is  a  law 
for  the  magnetic  circuit — namely,  m.m.f.  =(f>R,  where 
m.m.f.  is  the  magnetomotive  force  and  depends  on  TI, 
<f>  is  the  flux  threading  the  magnetic  circuit, 
R  is  the  reluctance  of  the  magnetic  circuit. 

The  most  convenient  unit  of  m.m.f.  would  have  been  the 
ampere-turn,  but  in  order  to  conform  to  the  definition  of  potential 
as  used  in  hydraulic  and  electric  circuits,  another  unit  has  to  be 
adopted. 

The  difference  of  potential  in  centimeters  between  two  points  in 
a  hydraulic  circuit  is  the  work  done  in  ergs  in  moving  unit  mass 
of  water  from  one  point  to  the  other,  and  the  difference  of  mag- 
netic potential  (m.m.f.)  between  two  points  in  a  magnetic  circuit 
is  the  work  done  in  ergs  in  moving  a  unit  pole  from  one  point 
to  the  other. 

Let  a  unit  pole,  which  has  4n  lines  of  force,  be  moved  through 
the  electro-magnet  from  A  to  B  in  a  time  of  t  seconds,  then  an 

e.m.f.  E=  —  Tx~j-  c.g.s.  units  will  be  generated  between  a  and 

b.  In  order  to  maintain  the  current  7  constant  against  this 
e.m.f.  an  amount  of  work  =EI  ergs  per  second  must  be  done; 
so  that  the  m.m.f.  between  A  and  B 

=  EIt  ergs, 

It  ergs, 
ergs  when  7  is  in  c.g.s.  units, 


=  j~  77  ergs  when  7  is  in  amperes, 

therefore  the  unit  of  m.m.f.  is  not  the  ampere-turn,  but  is  equal 
to  -^  ampere-turns. 

It  must  be  understood  that  this  m.m.f.  is  what  might  be 
called  the  generated  m.m.f.,  thus  in  the  electro-magnet  shown 


MAGNETIC  INDUCTION  5 

in  Fig.  5  the  generated  m.m.f.  is  equal  to  y~  TI,  but  the  effective 

m.m.f.  between  A  and  B  is  equal  to  this  generated  m.m.f. 
minus  the  m.m.f.  necessary  to  send  the  magnetic  flux  round  the 
iron  part  of  the  magnetic  circuit.  Take  for  example  the  extreme 
case  shown  in  Fig.  6,  where  the  core  is  bent  round  to  form  a 
complete  annular  ring.  The  generated  m.m.f.  between  the 

points  A  and  B  =  Tr>  TI,  but  A  is  the  same  point  as  B  so  that 

there  can  be  no  difference  of  magnetic  potential  between  them, 
therefore  all  the  generated  m.m.f.  is  used  up  in  sending  the 


FIG.  5. — Magnetic  circuit.  FIG.  6. — Closed  magnetic  circuit. 


flux  (f>  through  the  ring  itself.  By  means  of  such  a  ring  the 
magnetic  materials  used  in  electrical  machinery  are  tested;  the 
cross-section  S  of  the  ring  arid  also  the  mean  length  I  are  known, 
and  for  a  given  generated  m.m.f.  the  flux  (f>  can  be  measured. 
Then  since 


m.m.f.  =<f)R 

therefore  ^.TI  =  d>  ~^  = 
lu  o 


,  from  which  k  can  be  found. 


B  is  the  flux  density  or  number  of  lines  per  square  centimeter, 
k  is  the  specific  reluctance  and  =  1  for  air, 
I  is  in  centimeters. 
For  an  air  path,  B,  the  flux  density  in  lines  per  square  centi- 

meter =  ~--—)  where  I  is  in  centimeters.     When  inch  units  are 


6  ELECTRICAL  MACHINE  DESIGN 

used,  so  that  I  is  in  inches,  and  the  flux  density  is  in  lines  per 
square  inch,  then 

TI 

B,  the  flux  density  in  lines  per  square  inch  =  3. 2-p*  (1) 

For  materials  like  iron,  k,  the  specific  reluctance,  is  much  less 
than  1,  and  the  value  of  k  varies  with  the  flux  density.  For 
practical  work  the  value  of  k  is  never  plotted;  it  is  more  con- 
venient to  use  curves  of  the  type  shown  in  Fig.  42,  page  47, 
which  curves  are  determined  by  testing  rings  of  the  particular 

TI 

material  and  plotting  B  in  lines  per  square  inch  against  -j-> 

where  I  is  in  inches. 


CHAPTER  II 
ARMATURE  WINDING 

7.  Definition  of  Armature  Winding. — In  Fig.  7  the  armature 
A  of  a  generator  is  revolving  in  the  magnetic  field  NS  in  the 
direction  of  the  arrow.  The  directions  of  the  e.m.fs.  which  are 
generated  in  the  conductors  of  the  armature  are  found  by  the 
three-finger  rule  and  shown  in  the  usual  way  by  crosses  and  dots. 
The  principal  purpose  of  the  armature  winding  is  to  connect  the 
armature  conductors  together  in  such  a  way  that  a  desired 
resultant  e.m.f.  can  be  maintained  between  two  points  which  are 
connected  to  an  external  circuit.  The  conductors  and  their 
interconnections  taken  together  form  the  winding. 


FIG.  7. — Direction  of  current  in 
a  D.-C.  generator. 


FIG.  8. — Two-pole  simplex 
Gramme  winding. 


8.  Gramme  Ring  Winding. — This  type  of  winding,  which  is 
shown  diagrammatically  in  Fig.  8,  was  one  of  the  first  to  be  used. 
Although  the  winding  is  now  practically  obsolete  it  is  mentioned 
because  of  its  simplicity,  and  because  it  shows  more  clearly 
than  does  any  other  type  of  winding  the  meaning  of  the  different 
terms  used  in  the  system  of  nomenclature.1 

The  two-pole  winding  shown  in  Fig.  8  is  the  simplest  type  of 
Gramme  winding;  it  has  only  two  paths  between  the  +  and  the 
—  brush  and  is  called  the  simplex  winding  to  distinguish  it  from 

1  The  system  of  nomenclature  adopted  in  this  chapter  is  that  of  Parshall 
and  Hobart. 

7 


8 


ELECTRICAL  MACHINE  DESIGN 


the  other  two  fundamental  Gramme  windings,  shown  in  Figs.  9 
and  10.  Inspection  of  these  latter  figures  shows  that  in  each 
of  these  cases  there  are  four  paths  between  the  +  and  the  - 
brush,  or  twice  as  many  as  in  the  case  of  the  simplex  winding; 
for  this  reason  they  are  called  duplex  windings.  There  is, 
however,  an  essential  difference  between  the  two  duplex  windings 
and  to  distinguish  between  them  it  is  necessary  to  define  the 
term  re-entrancy. 

9.  Re-entrancy. — -If  the  winding  shown  in  Fig.  8  be  followed 
round  the  machine  starting  at  any  point  b,  it  will  be  found  that 
the  winding  returns  to  the  starting-point,  or  is  re-entrant,  and 
that  before  it  becomes  re-entrant  every  conductor  has  been  taken 
in  once  and  only  once;  such  a  winding  is  called  a  singly  re-entrant 
winding. 


FIG.  9. — Doubly  re-entrant 
duplex  winding. 


FIG.  10. — Singly  re-entrant 
duplex  winding. 


If  the  winding  shown  in  Fig.  9  be  followed  round  the  machine 
starting  at  any  point  b,  it  will  be  found  to  be  re-entrant  when 
only  half  of  the  conductors  have  been  taken;  in  fact  the  winding 
is  simply  two  singly  re-entrant  windings  put  on  the  same  core, 
and  is  called  a  doubly  re-entrant  duplex  winding. 

If,  on  the  other  hand,  the  winding  shown  in  Fig.  10  be  followed 
round  the  machine  starting  at  any  point  6,  it  will  be  found  that 
it'  does  not  become  re-entrant  until  every  conductor  has  been 
taken  in  once  and  only  once;  it  is  therefore  a  singly  re-entrant 
duplex  winding. 

It  is  evidently  possible  to  carry  this  process  of  increasing  the 
number  of  paths  through  the  winding  much  further  so  as  to  get 
multiplex  multiply  re-entrant,  multiplex  singly  re-entrant,  and 
many  other  combinations;  but  such  windings  are  rarely  to  be 
found  in  modern  machines,  in  fact  even  duplex  windings  are 


ARMATURE  WINDING 


seldom  used  except  for  large-current  low-voltage  machines. 
In  such  machines  the  large  current  entering  the  brush  is  divided 
up  and  passes  through  the  several  paths,  so  that  during  commu- 
tation the  current  which  is  being  commutated  is  only  half  of 
what  it  would  have  been  had  a  simplex  winding  been  used.  This 
is  shown  at  the  positive  brush,  Fig.  10,  where  it  will  be  seen  that 
only  the  current  in  coil  5,  or  half  of  the  total  current,  is  being 
commutated  at  that  instant. 

In  the  case  of  a  duplex  winding  the  brush  must  be  wide  enough 
to  cover  two  segments  in  order  to  collect  current  from  all  four 
paths. 

10.  Objections  to  the  Gramme  Winding. — In  the  case  of  small 
machines  it  is  difficult  to  find  space  below  the  core  for  the  return 
part  of  the  winding  without  making  the  diameter  of  the  machine 
unnecessarily  large;  while  in  the  case  of  large  machines,  where 
the  winding  is  made  of  heavy  strip  copper,  it  is  difficult  to 
remove  and  replace  damaged  coils. 

The  number  of  coils  and  commutator  segments  is  twice  that 
required  for  a  machine  of  the  same  voltage  and  with  the  other 
type  of  winding,  namely  the  drum  winding. 


FIG.  11. — Coil  for  drum  winding. 

In  many  cases  the  active  part  of  a  coil  is  only  a  small  portion 
of  the  total  coil  since  the  side  and  return  connections  do  not  cut 
lines  of  force. 

Since  the  whole  winding  lies  close  to  the  iron  of  the  core  the 
coefficient  of  self-induction  of  the  coils  is  large  and  the  machine 
on  that  account  is  liable  to  spark. 

11.  Drum  Winding. — This  winding  was  developed  to  over- 
come the  objections  to  the  Gramme  winding.  In  the  simplest 


10 


ELECTRICAL  MACHINE  DESIGN 


case  two  conductors  are  joined  together  to  form  a  coil  of  the 
shape  shown  in  Fig.  11.  This  coil  is  placed  on  the  machine  in 
such  a  way  that  when  one  side  a  of  the  coil  is  under  a  north  pole, 
the  other  side  b  is  under  the  adj  acent  south  pole,  therefore  both 
sides  of  the  coil  are  active  and  the  e.m.fs.  generated  in  the  two 
sides  act  in  the  same  direction  round  the  coil.  Since  each  coil 
consists  of  at  least  two  conductors,  the  total  number  of  con- 
ductors for  a  drum  winding  must  be  even. 

Fig.    12  shows  a  two-pole    simplex    singly  re-entrant  drum 
winding  with  16  conductors.     It  might  seem  that  conductors 


FIG.  12. — Two-pole  simplex  singly  re-entrant  drum  winding. 

which  are  exactly  opposite  to  one  another  should  be  connected 
in  series  to  form  a  coil,  so  that  conductor  1  should  be  connected 
to  conductor  9  and  then  back  to  conductor  2,  but  a  few  trials 
will  show  that  in  order  to  get  a  singly  re-entrant  winding  it  is 
necessary  to  make  the  even  conductors  the  returns  for  the  odd. 
Starting  then  at  conductor  1  the  winding  goes  to  the  nearest  even 
conductor  to  that  which  is  exactly  opposite,  namely  conductor 
8,  then  returning  back  to  the  south  pole  the  next  odd  conductor 
is  number  3,  which  again  is  connected  to  conductor  10,  and  so  on; 
so  that  the  complete  winding  can  be  represented  by  the  following 
table: 

l-8_3-10_5-12_7-14_9-16_ll-2_13-4_15-6_l, 

which  shows  clearly  that  the  winding  is  re-entrant,  and  also 
that  every  conductor  has  been  taken  in  once  and  only  once. 


ARMATURE  WINDING 


11 


The  connections  of  this  winding  to  the  commutator  are  shown 
in  Fig.  12. 

Fig.  13  is  another  method  adopted  to  show  the  connections  of 
the  same  winding  and  is  obtained  by  splitting  Fig.  12  at  xy  and 
opening  it  out  on  to  a  plane.  This  gives  what  is  called  the 
developed  winding  and  shows  clearly  the  shape  of  the  coil  which 
is  used.  If  Fig.  13  be  cut  out  and  bent  around  a  drum  it  will 
give  the  best  possible  representation  of  a  drum  winding. 

Inspection  of  Figs.  12  and  13  shows  that,  just  as  in  the  case  of 
the  simplex  Gramme  winding,  there  are  two  paths  between  the 
+  and  the  —  brush. 


1 

14 

12 

11 

10 

9 

8 
,     ^ 

7    6 
(      \ 

,15> 

4 

3 

,     2 

1 

i 

N 

I 

S 

FIG.  13. 


B-  B-f 

-Developed  two-pole  simplex  singly  re-entrant  drum  winding. 


12.  The  E.M.F.  Equation.— If 

(f)a  is  the  flux  per  pole  which  is  cut  by  the  armature  conductors, 

p  is  the  number  of  poles, 

Pi  is  the  number  of  paths  through  the  armature, 

Z  is  the  total  number  of  face  conductors  on  the  armature  surface, 

r.p.m.  is  the  speed  of  the  armature  in  revolutions  per  minute, 

then  one  conductor  cuts  (f>ap  lines  per  revolution 

or, 

.      r.p.m. 
<pap  — x/x —  lines  in  one  second. 

i? 

Since  the  number  of  conductors  between  a+  and  a—  brush  =  — 

the  e.m.f.  between  the  terminals  in  volts 

=  -^p-^-10-  (2) 

,«      /    **>tr          /?  C\  \      ' 


12 


ELECTRICAL  MACHINE  DESIGN 


The  number  of  poles  and  paths  is  determined  by  the  designer  of 
the   machine. 

13.  Multipolar  Machines. — One  of  the  easiest  ways  by  which 
to  get  several  paths  through  the  winding  is  to  build  multipolar 


FIG.  14. — Six-pole  simplex  singly  re-entrant  multiple  drum  winding. 


I 


FIG.  15. — Part  of  a  six-pole  simplex  singly  re-entrant  multiple  drum  winding. 

machines,  thus  Fig.  14  shows  a  six-pole  drum  winding  which 
has  six  paths  in  parallel  between  the  +  and  the  —  terminals. 
There  are  three  +  and  three  —  brushes  and  like  brushes  are 
connected  together  outside  of  the  machine  at  T+  and  T-  .  The 


ARMATURE  WINDING  13 

diagram  which  is  used  in  this  case  is  a  slight  modification  of  the 
developed  diagram  and  gets  over  the  difficulty  of  splitting  the 
winding.  Fig.  14  is  rather  complicated  and  will  be  explained  in 
detail. 

Figure  15  shows  the  armature  conductors,  the  poles  and  the 
commutator  of  the  same  machine.  There  are  two  conductors  in 
each  slot  so  that  a  section  through  one  of  the  slots  is  as  shown  at 
S,  Fig.  15;  the  winding  lies  in  two  layers  and  is  called  a  double 
layer  winding.  In  Fig.  14  there  are  24  slots  and  48  conductors; 
a  conductor  in  the  top  half  of  a  slot  is  an  odd-numbered  conductor 
and  that  in  the  bottom  half  of  a  slot  is  an  even-numbered  con- 
ductor, so  that,  since  the  even  conductors  are  the  returns  for  the 
odd,  each  coil  has  one  side  in  the  top  of  one  slot  and  the 
other  side  in  the  bottom  of  the  slot  which  is  one  pole  pitch 
further  over.  The  coils  are  all  alike  and  are  made  on  the  same 
former;  a  few  of  the  coils  are  shown  in  place  in  Fig.  15,  where 
conductors  that  are  in  the  top  layer  are  represented  by  heavy  lines 
while  those  in  the  bottom  layer  are  represented  by  dotted  lines. 

14.  Equalizer  Connections. — In  the  winding  shown  in  Fig.  14 
there  are  six  paths  in  parallel  between  the  +  and  the  —  terminals, 
and  it  is  necessary  that  the  voltages  in  all  six  paths  be  equal, 
otherwise  circulating  currents  will  flow  through  the  machine. 
In  Fig.  16,  for  example,  is  shown  a  case  where,  due  to  wear  in  the 
bearings,  the  armature  is  not  central  with  the  poles,  and  there- 
fore the  flux  density  in  the  air  gap  under  poles  A  is  greater  than 
that  in  the  air  gap  under  poles  B,  so  that  the  conductors  under 
poles  A  will  have  higher  voltages  generated  in  them  than  those 
that  are  under  poles  B,  and  the  voltage  between  brushes  c  and  d 
will  be  greater  than  that  between  brushes/  and  g.  Since  c  and/ 
are  connected  together,  as  also  are  d  and  g,  a  circulating  current 
will  flow  from  c  to  /,  through  the  winding  to  g,  then  to  d  and 
back  through  the  winding  to  c,  as  shown  diagrammatically  at 
C,  Fig.  16. 

Since  the  circulating  currents  pass  through  the  brushes,  some 
of  the  brushes  will  have  to  carry  more  current  than  they  were 
designed  for,  and  sparking  will  result.  To  prevent  the  circulating 
current  from  having  any  large  value  it  is  necessary  to  prevent 
unequal  flux  distribution  in  the  air  gaps  under  the  poles.  This 
can  be  done  by  setting  up  the  machine  carefully,  taking  off  the 
outside  connections  T+  and  T_  between  the  brushes,  and  adj  ust- 
ing  the  thickness  of  the  air  gaps  under  the  different  poles  until 


14 


ELECTRICAL  MACHINE  DESIGN 


the  voltages  between  +  and  —  brushes  are  all  equal,  the  machine 
being  fully  excited  and  running  at  full  speed  and  no  load. 

It  is  impossible,  to  eliminate  entirely  this  circulating  current, 
but  its  effect  must  be  minimized.  This  is  done  by  providing 
a  low  resistance  path  of  copper  between  the  points  c  and  /  and 
also  between  d  and  g,  inside  of  the  brushes,  so  that  the  circulating 
current  will  pass  around  this  low-resistance  path  rather  than 
through  the  brushes.  It  must  be  understood  that  the  equal- 
izer connections,  as  these  low-resistance  paths  are  called,  do 
not  eliminate  the  circulating  current,  but  merely  prevent  it 


/     9 
C 


FIG.  16. — Machine  with  unequal  air-gaps  to  show  the  action  of  equalizer 

connections. 

from  passing  through  the  brushes.  When  the  armature  in  Fig. 
16  revolves  into  another  position  a  different  set  of  conductors 
have  to  be  supplied  with  equalizers,  and  in  order  that  the 
machine  may  be  properly  equalized  in  all  positions  of  the  arma- 
ture, all  points  which  ought  to  be  at  the  same  potential  at  any 
instant  must  be  connected  together. 

Figure  14  is  the  complete  diagram  showing  all  the  windings 
and  also  the  equalizers.  It  is  not  necessary  to  equalize  all  the 
coils,  because  when,  as  in  Fig.  14,  the  brush  is  on  a  coil  which  is 
not  directly  connected  to  an  equalizer,  there  is  still  a  path  of 
lower  resistance  than  that  through  the  brushes,  namely  round 
one  turn  of  the  winding  and  then  through  the  equalizer  connec- 
tion. It  is  usual  in  practice  to  put  in  about  30  per  cent,  of  the 
maximum  possible  number  of  equalizer  connections. 


ARMATURE  WINDING 


15 


The  developed  diagram  corresponding  to  that  of  Fig.  14  is 
shown  in  Fig.  17;  the  only  change  that  has  been  made  is  that  the 
equalizer  connections  have  been  put  at  the  back  of  the  machine 
where  they  can  be  easily  got  at  for  repair.  When  these  connec- 
tions are  placed  behind  the  commutator  it  is  impossible  to  get 
at  them  for  repair  without  disconnecting  the  commutator  from 
the  armature  winding. 

When  an  armature  is  supplied  with  equalizer  connections  each 
brush  will  carry  its  proper  share  of  the  total  current,  because  at 


•.•  +  •••*•••  +  ••• 


II 

FIG.  17. — Six-pole  simplex  singly  re-entrant  drum  winding. 

one  side  the  brushes  are  all  connected  together  through  the 
terminal  connections  and  at  the  other  side  through  the  equalizer 
connections,  so  that  the  voltage  drop  across  each  brush  is  the 
same,  and  since  the  brushes  are  all  made  of  the  same  material 
they  must  have  the  same  current  density. 

15.  Short  Pitch  Windings. — In  Fig.  14  the  two  sides  of  each 
coil  are  exactly  one  pole  pitch  apart;  such  a  winding  is  said  to  be 
full  pitch.  In  Fig.  18  is  shown  a  winding  in  which  the  two  sides 
of  each  coil  are  less  than  one  pole  pitch  apart;  such  a  winding  is 
said  to  be  short  pitch.  Fig.  19  shows  the  developed  diagram 
for  this  short-pitch  winding  at  the  instant  when  the  coils  in  the 
neutral  zone  are  short-circuited.  It  will  be  seen  that  the  effective 
width  of  the  neutral  zone  has  been  reduced  by  the  angle  a;  this 
disadvantage,  however,  is  compensated  for  by  the  fact  that  the 
conductors  of  the  coils  which  are  short-circuited  at  any  instant 
are  not  in  the  same  slot.  This,  as  shown  in  Art.  67  page  82, 
lessens  the  mutual  induction  between  the  short-circuited  coils 
and  tends  to  improve  commutation.  Shortening  the  pitch  by 
more  than  one  slot  decreases  the  neutral  zone  but  does  not 


16 


ELECTRICAL  MACHINE  DESIGN 


further  decrease  the  mutual  induction,  so  that  there  is  no 
advantage  in  shortening  the  coil  pitch  more  than  one  slot,  but 
rather  the  reverse.  Since  there  are  seldom  less  than  12  slots 
per  pole  the  effect  of  the  shortening  of  the  pitch  on  the  generated 
voltage  and  on  the  armature  reaction  can  be  neglected. 


FIG.  18. — Six-pole  simplex  singly  re-entrant   short-pitch   multiple   drum 

winding. 


FIG.  19. — Corresponding  developed  drum  winding. 


16.  Multiple  Windings. — The  windings  shown  in  Figs.  14  and 
18  have  the  same  number  of  circuits  through  the  armature  as 
there  are  poles.  Had  they  been  duplex  windings  they  would 
have  had  twice  as  many  circuits.  When  the  winding  has  a 
number  of  circuits  which  is  a  multiple  of  the  number  of  poles 


ARMATURE  WINDING 


17 


it  is    called  a   multiple  winding    to   distinguish    it    from   that 
described  in  the  next  article  which  is  called  a  series  winding. 

Since  windings  that  are  not  simplex  and  singly  re-entrant  are 
very  rare,  these  two  terms  are  generally  left  out,  so  that,  unless 
it  is  actually  stated  to  the  contrary,  all  windings  are  assumed 
to  be  simplex  singly  re-entrant,  and  the  windings  shown  in 
Figs.  14  and  18  would  be  called  six-pole  multiple  drum  windings. 


FIG.  20. — Six-pole  series  progressive  drum  winding. 


FIG.  21. — Small  part  of  the  above  winding. 

17.  Series  Windings. — It  is  possible  to  wind  multipolar 
machines  so  that  there  are  only  two  paths  through  the  armature 
winding.  Such  windings  are  called  series  windings  and  an 
example  of  one  is  shown  in  Fig.  20  for  a  six-pole  machine;  in 
Fig.  21  a  small  portion  of  the  winding  is  shown  to  make  the 
complete  diagram  clearer. 


18 


ELECTRICAL  MACHINE  DESIGN 


If  the  winding  be  followed  through,  starting  from  the  —  brush, 
it  will  be  seen  that  there  are  only  two  circuits  through  the 
armature,  and  that  only  two  brushes  are  required.  At  the 
instant  shown  in  Fig.  21  the  -  •  brush  is  short-circuiting  two 
commutator  segments  and  in  so  doing  short  circuits  three 
coils.  Since  the  points  a,  b  and  c  are  all  at  the  same  poten- 
tial it  is  possible  to  put  —  brushes  at  each  of  these  points,  so 
that  the  current  will  not  be  collected  from  one  set  of  brushes 
but  from  three;  this  will  allow  the  use  of  a  commutator  of  1/3  of 
the  length  of  that  required  when  only  one  set  of  positive  and 
one  set  of  negative  brushes  are  used.  A  machine  with  a  series 
winding  will  therefore  have  in  most  cases  the  same  number  of 
brush  sets  as  there  are  poles. 


FIG.  22.  —  Six-pole  series  retrogressive  drum  winding. 


It  may  be  seen  from  Fig.  21  that  the  number  of  commutator 
segments  must  not  be  a  multiple  of  the  number  of  poles  otherwise 
the  winding  would  close  in  one  turn  round  the  machine;  to  be 
singly  re-entrant  the  winding  must  progress  by  one  commutator 
segment,  as  shown  in  Fig.  20,  or  retrogress  by  one  commutator 
segment,  as  shown  in  Fig.  22,  each  time  it  passes  once  round  the 
armature,  the  condition  for  this  is  that  $,  the  number  of 

commutator  segments,    =&~+l,   where   k   is  a   whole  number 

Zj 

and  p  the  number  of  poles.     When  the  —  sign  is  used  the  winding 
is  progressive,  as  in  Fig.  20,  where  the  number  of  commutator 


ARMATURE  WINDING  19 

segments  is  23,  and  when  the  +  sign  is  used  the  winding  is  retro- 
gressive, as  in  Fig.  22,  where  the  number  of  commutator  segments 
is  25. 

The  paragraph  in  Art.  14,  page  15,  on  the  division  of  the 
total  current  of  the  machine,  holds  to  a  certain  extent  for 
the  series  winding  also;  the  one  side  of  all  the  brushes  are 
connected  together  through  the  short-circuited  coils,  as  shown 
in  Fig.  21,  while  the  other  side  of  the  same  brushes  are  con- 
nected together  through  the  terminal  connections.  It  is  im- 
portant to  notice,  however,  that  since  the  number  of  com- 

T) 

mutator  segments  S  is  not  a  multiple  of  ~>   the  number  of  pairs 

£i 

of  poles,  and  since  the  brushes  of  like  polarity  are  spaced  two 
pole  pitches  apart,  a  kind  of  selective  commutation  will  take 
place,  thus  when,  as  shown  in  Fig.  21,  brush  a  is  short-circuiting 
a  set  of  three  coils  in  series,  brush  6  has  just  begun  to  short-circuit 
an  entirely  different  set  of  three  coils  in  series  and  brush  c  has 
nearly  finished  short-circuiting  still  another  set  of  three  coils  in 
series. 

The  series  winding  has  the  great  advantage  that  equalizers 
are  not  required,  since,  as  shown  in  Fig.  21,  the  winding  is  already 
equalized  by  the  coils  themselves,  so  that  there  can  be  no  circu- 
lating current  passing  through  the  brushes;  further 'there  can 


FIG.  23. — Coils  with  several  turns. 

be  no  circulating  current  in  the  machine  due  to  such  causes  as 
unequal  air  gaps  because  each  circuit  of  the  winding  is  made  up 
of  conductors  in  series  from  under  all  the  poles.  On  account  of 
this  fact,  and  also  because  of  the  property  that  only  two  sets  of 
brushes  are  required,  the  series  winding  is  used  for  D.-C.  railway 
motors,  because  in  a  four-pole  railway  motor  the  two  brushes 
can  be  set  90  degrees  apart  so  as  to  have  both  sets  of  brushes 
above  the  commutator,  where  they  can  be  easily  inspected  from 
the  car. 


20  ELECTRICAL  MACHINE  DESIGN 

18.  Lap  and  Wave  Windings. — From  the  appearance  of  the 
individual  coils  of  the  two  windings,  Figs.  14  and  20,  the  former 
is  sometimes  called  a  lap  winding  and  the  latter *a  wave  winding. 
It  must  be  understood,  however,  that  each  of  the  coils  shown  in 
these  diagrams  may  consist  of  more  than  one  turn  of  wire,  thus 
Fig.  23  shows  both  a  lap  and  a  wave  coil  with  several  turns  per 
coil,  so  that  the  terms  lap  and  wave  apply  only  to  the  connec- 
tions to  the  commutator  and  not  to  the  shape  of  the  coil  itself; 
the  terms  multiple  and  series  are  more  generally  used. 

19.  Shop  Instructions. — It  would  be  a  mistake  to  send  winding 
diagrams  such  as  those  described  in  this  chapter  into  the  shop 
and  expect  the  men  in  the  winding  room  to  connect  up  a  machine 
properly  from   the   information   given   there;   the   instructions 
must  be  given  in  much  simpler  form.     For  a  winding  such  as 
that  shown  in  Fig.  17  the  shop  instructions  would  read:  "Put 
the  coil  in  slots  1  and  5  and  the  commutator  connections  in 
segments  1  and  2,"  where  the  position  of  segment  1  relative  to 
that  of  slot  1  is  fixed  by  the  shape  of  the  end  of  the  coil. 
All  the  coils  are  made  on  formers  and  are  exactly  alike,  so  that, 
having  the  first  coil  in  place,  the  workman  can  go  straight  ahead 
and  put  in  the  other  coils  in  a  similar  manner. 

In  the  case  of  a  winding  such  as  that  shown  in  Fig.  20,  the 
instructions  would  read:  " Put  the  coil  in  slots  1  and  5  and  the 
commutator  connections  in  segments  1  and  9,"  where  the  position 
of  segment  1  relative  to  that  of  slot  1  is  again  fixed  by  the  shape 
of  the  coil. 

20.  Duplex  Multipolar  Windings. — The  multipolar  windings 
discussed  so  far  have  all  been  simplex  and  singly  re-entrant. 
It  is  evident  that  both  multiple  and  series  windings  can  be  made 
duplex  if  necessary;  such  windings  can  easily  be  drawn  from 
the  information  already  given  in  this  chapter  and  no  special 
discussion  of  them  is  necessary. 

21.  Windings  with  Several  Coil  Sides  in  One  Slot.— There  are 
generally  more  coils  than  there  are  slots.     Fig.  24  shows  part  of 
the  winding  diagram  for  a  machine  which  has  a  multiple  wind- 
ing with  four  coil  sides  in  each  slot  and  two  turns  per  coil,  and 
Fig.  25  shows  part  of  the  winding  diagram  for  a  series  wound 
machine  also  with  four  coil  sides  in  each  slot   and  two  turns 
per  coil.     A  section  through  one  slot  in  each  case  is  shown  in 
Fig.  26;  there  are  eight  conductors  per  slot  and  conductors  are 
numbered  similarly  in  Figs.  25  and  26.     In  each  case  there  are 


ARMATURE  WINDING 


21 


FIG.  24. — Multiple  winding  with  four  coil  sides  per  slot  and  two  turns  per 

coil. 


345 


J 1 1 1 1 1 L 


FIG  25. — Series  winding  with  four  coil  sides  per  slot  and  two  turns  per  coil. 


1256 


3478 


FIG.  26. — Section  through  one  slot  of  the  above  windings. 


22  ELECTRICAL  MACHINE  DESIGN 

two  commutator  segments  to  a  slot  since  the  number  of  commuta- 
tor segments  is  always  the  same  as  the  number  of  coils,  in  fact 
a  coil  may  be  denned  as  the  winding  element  between  two 
commutator  segments. 

22.  Number  of  Slots  and  Odd  Windings. — For  series  or  wave 
windings  the  number  of  coils  =  S,  the  number  of  commutator 

segments,  =  k^+l,  therefore  the  number  of  coils  must  always  be 
u 

odd,  and  the  number  of  slots  should  also  be  odd.  Even  when  an 
odd  number  of  slots  is  used  it  is  not  always  possible  to  get  a  wave 
winding  without  some  modification.  Suppose,  for  example,  that 
a  110-volt  four-pole  machine  has  49  slots  and  two  conductors  per 

slot,  then  the  number  of  coils  =  49  =  24^  +  1,  which  will   give  a 

•  satisfactory  winding;   when  wound  for  220  volts  the  machine 
requires  twice  the  number  of  conductors,  or  four  conductors  per 

slot,  so  that  the  number  of  coils  =  98  =  49^  +  0  which  will  not  give 

2i 

a  wave  winding.  In  such  a  case,  however,  the  winding  can 
be  made  wave  by  cutting  out  one  coil  so  that  the  machine  has 
really  97  coils  instead  of  98,  and  has  also  97  commutator  seg- 
ments; the  extra  coil  is  put  into  the  machine  for  the  sake  of 
appearance  but  is  not  connected  up,  its  two  ends  are  taped  so 
as  to  completely  insulate  the  coil,  and  it  is  called  a  dead  coil. 

When  the  armature  is  large  in  diameter  it  is  built  in  segments 
as  described  in  Art.  28,  page  28.  In  such  a  case  it  is  difficult 
to  get  an  odd  number  of  slots  on  the  armature;  indeed,  it  can  only 
be  done  when  the  number  of  segments  that  make  up  one  complete 
ring  of  the  armature  and  also  the  number  of  slots  per  segment 
are  both  odd  numbers;  however,  for  reasons  to  be  discussed 
under  commutation,  series  or  wave  windings  are  seldom  found 
in  large  machines. 

For  multiple  or  lap  windings  the  number  of  slots  must 
be  multiple  of  half  the  number  of  poles  if  equalizers  are  to 
be  used;  this  can  be  ascertained  from  Fig.  16,  where  it  is  seen 
that  in  the  case  of  a  six-pole  machine  the  equalizers  must  each 
connect  together  three  points  on  the  armature  exactly  two  pole 
pitches  apart  from  one  another.  It  is  found,  however,  that 
small  four-pole  machines  with  multiple  windings  run  sparklessly 
without  equalizers,  and  since  the  only  condition  that  limits  a 
multiple  winding  without  equalizers  is  that  the  number  of  con- 


ARMATURE  WINDING  23 

ductors  be  even,  for  such  small  machines  the  same  punching  is 
used  as  for  the  machine  with  the  series  winding,  namely,  a  punch- 
ing having  an  odd  number  of  slots;  the  number  of  conductors  will 
be  even  since  the  winding  is  double  layer,  and  has  therefore  a 
multiple  of  two  conductors  per  slot.  By  the  use  of  the  same 
punching  for  both  multiple  and  series  windings,  a  smaller  stock 
of  standard  parts  needs  to  be  kept,  quicker  shipment  can  be 
made,  and  lower  selling  prices  given  for  small  motors,  than  if 
different  punchings  were  used.  In  the  case  of  large  machines  it 
is  best  to  make  the  winding  such  that  equalizers  can  be  used, 
because  the  sparking  caused  by  the  want  of  equalizers  becomes 
worse  as  the  number  of  poles  and  as  the  output  of  the  machine 
increases. 


CHAPTER  III 
CONSTRUCTION  OF  MACHINES 

The  construction  of  electrical  machinery  is  really  a  branch  of 
mechanical  engineering  but  it  is  one  which  requires  considerable 
knowledge  of  electrical  phenomena. 

Figure  27  shows  the  type  of  construction  that  is  generally 
adopted  for  D.-C.  machines  of  outputs  up  to  100  h.p.  at  600 
r.p.m. 

23.  The  Armature. — M,  the  armature  core,  is  built  up  of 
laminations  of  sheet  steel  0.014  in.  thick,  the  thinner  the  lamina- 
tions the  lower  the  eddy  current  loss  in  the  core,  but  sheets 
thinner  than  0.014  in.  are  flimsy  and  difficult  to  handle. 

The  laminations  are  insulated  from  one  another  by  a  layer  of 
varnish  and  are  mounted  directly  on  the  shaft  of  the  machine 
and  held  there  by  means  of  a  key,  as  shown  at  K.  It  will  be 
noticed  that  in  the  key-way  K  there  is  a  small  notch,  called 
a  marking  notch,  the  object  of  which  is  to  ensure  that  the 
burrs  on  the  punchings  all  lie  the  same  way;  it  is  impossible  to 
punch  out  slots  and  holes  without  burring  over  the  edge,  and 
unless  these  burrs  all  lie  in  the  same  direction  a  loose  core  is 
produced. 

The  laminations  are  punched  on  the  outer  periphery  with 
slots  F  which  carry  the  armature  coils  G.  The  type  of  slot 
shown  is  that  which  is  in  general  use  and  is  called  the  open  slot. 
The  other  type  which  is  sometimes  used  is  closed  at  the  top;  the 
coils  in  this  case  have  to  be  pushed  in  from  the  ends.  The  open 
slot  has  the  advantage  that  the  armature  coils  can  be  fully  insu- 
lated before  being  put  into  the  machine,  and  that  the  coils  can 
be  taken  out,  repaired,  and  replaced,  in  the  case  of  a  break- 
down, more  easily  than  if  the  closed  type  of  slot  had  been 
adopted. 

The  armature  core  is  divided  into  blocks  by  means  of  brass 
vent  segments,  shown  at  P\  the  object  of  the  vent  ducts  so 
produced  is  to  allow  free  circulation  of  air  through  the  machine 
to  keep  it  cool;  they  divide  the  core  into  blocks  less  than  3  in. 
thick  and  are  approximately  3/8  in.  wide;  narrower  ducts  are 

24 


CONSTRUCTION  OF  MACHINES  25 

not  very  effective  and  are  easily  blocked  up,  while  wider  ducts 
do  not  give  increased  cooling  effect  and  take  up  space  which 
might  be  filled  with  iron. 

The  vent  segments  are  mounted  directly  on  the  shaft,  and, 
along  with  the  laminations  of  the  core,  are  clamped  between  two 
cast-iron  end  heads  N.  These  end  heads  carry  the  coil  supports 
L  which  are  attached  by  arms  shaped  so  as  to  act  as  fans  and 
maintain  a  circulation  of  air  through  the  machine. 

The  armature  coils  are  held  against  centrifugal  force  by  steel 
band  wires,  five  sets  of  which  are  shown. 

24.  Poles  and  Yoke. — The  armature  revolves  in  the  magnetic 
field  produced  by  the  exciting  coils  A  which  are  wound  on  and 
insulated  from  the  poles  B.  In  Fig.  27  the  poles  are  of 
circular  cross-section  so  as  to  give  the  required  area  for  the 
flux  with  the  minimum  length  of  mean  turn  of  the  field  coil. 
They  are  made  of  forged  steel  and,  attached  to  them  by  means 
of  screws,  there  is  a  laminated  pole  face  E  made  of  sheet  steel 
0.025  in.  thick,  to  prevent,  as  far  as  possible,  eddy  currents  in  the 
pole  faces. 

The  pole  face  laminations  are  stacked  up  to  give  the  neces- 
sary axial  lejigth  and  are  held  together  by  four  rivets.  In  Fig. 
27  it  will  be  seen  that  each  end  lamination  has  a  projection  on  it 
for  the  purpose  of  supporting  the  field  coil. 

The  axial  length  of  the  pole  in  the  machine  shown  is  3/8  in. 
shorter  than  the  axial  length  of  the  armature  core.  This  is  done 
to  enable  the  revolving  part  of  the  machine  to  oscillate  axially 
and  so  prevent  the  journals  and  bearings  from  wearing  in  grooves. 
In  order  that  the  armature  may  oscillate  freely  it  is  necessary 
that  the  reluctance  of  the  air  gap  does  not  change  between  the 
two  extreme  positions,  the  condition  for  which  is  that  the 
armature  core  be  longer  or  shorter  axially  than  the  pole  face  by 
the  amount  to  be  allowed  for  oscillation,  which  is  usually  3/8  in. 
for  motors  up  to  50  h.  p.  at  900  r.p.m.,  and  1/2  in.  for  larger 
machines. 

The  poles  are  attached  to  the  yoke  C  by  means  of  screws, 
the  yoke  also  carries  the  bearing  housings  D  which  stiffen  the 
whole  machine  so  that  the  yoke  need  not  have  a  section  greater 
than  that  necessary  to  carry  the  flux. 

The  housings  and  yoke  are  clamped  together  by  means  of 
through  bolts,  and  the  construction  must  be  such  that  the 
housings  are  capable  of  rotation  relative  to  the  yoke  through 


26 


ELECTRICAL  MACHINE  DESIGN 


CONSTRUCTION  OF  MACHINES  27 

90  or  180  degrees  in  order  that  the  machine,  usually  a  small 
motor,  may  be  mounted  on  the  wall  or  on  the  ceiling.  This 
rotation  of  the  bearings  is  necessary  in  such  cases  because,  since 
the  machines  are  lubricated  by  means  of  oil  rings,  the  oil  wells 
must  be  always  below  the  shaft. 

25.  Commutator. — The  commutator  is  built  up  of  segments 
J  of  hard  drawn  copper  insulated  from  one  another  by  mica 
which    varies   in   thickness   from   0.02   to   0.06   in.,    depending 
on  the  diameter  of  the  commutator  and  the  thickness. of  the 
segment.     The  mica  used  for  this  purpose  must  be  one  of  the 
soft  varieties,  such  as  amber  mica,  so  that  it  will  wear  equally 
with  the  copper  segments. 

The  segments  of  mica  and  copper  are  clamped  between  two 
cast-iron  V-clamps  S  and  insulated  therefrom  by  cones  of 
micanite  1/16  in.  thick.  The  commutator  shell,  as  the  clamps 
and  their  supports  are  called,  is  provided  with  air  passages  R 
which  help  to  keep  the  machine  cool. 

The  commutator  segments  are  connected  to  the  armature 
winding  by  necks  or  risers  H  which,  in  all  modern  machines, 
have  air  spaces  between  them  as  shown,  so  that  air  will  be  drawn 
across  the  commutator  surface  and  between  the  risers  by  the 
fanning  effect  of  the  armature.  This  air  is  very'  effective  in 
cooling  the  commutator. 

26.  Bearings. — The  construction  of  a  typical  bearing  is  shown 
in  detail  and  is  self-explanatory.    The  points  of  interest  are:  the 
projection  T  on  the  oil-hole  cover,  the  object  of  which  is  to  keep 
the   oil  ring  from  rising   and  resting  on  the  bushing;  the   oil 
slingers  on  the  shaft,  which  prevent  the  oil  from  creeping  along 
the  shaft  and  leaving  the  bearing  dry;  the  bearing  construction 
with  a  liner  of  special  bearing  metal,  which  is  a  snug  fit  in  the 
bearing  shell   and  which  can  readily  be  removed  and  replaced 
when  worn;  the  method  adopted  for  draining  the  oil  back  into 
the  oil  well.     The  level  of  the  oil  is  shown  and  it  will  be  seen  that 
it  is  in  contact  with  a  large  portion  of  the  bearing  shell  and  is 
therefore  well  cooled.     The  oil  may  be  drained  out  when  old 
and  dirty  by  taking  out  the  plug  shown  at  the  bottom.     There 
is  a  small  overflow  at  U  which  prevents  the  bearing  from  being 
filled  too  full. 

The  brushes  are  carried  on  studs  which  are  insulated  from  the 
rocker  arm  V.  The  rocker  arm  is  carried  on  a  turned  seat  on 
the  bearing  and  can  be  clamped  in  a  definite  position. 


28 


ELECTRICAL  MACHINE  DESIGN 


27.  Slide  Rails. — When  the  machine  has  to  drive  or  be  driven 
by  a  belt,  the  feet  of  the  yoke  are  slotted  as  shown,  so  that  it  can 
be  mounted  on  rails  and  a  belt-tightening  device  supplied. 

28.  Large  Machines. — For  large  machines  the  type  of  con- 
struction is  somewhat  different  from  that  already  described; 
Fig.  28  shows  the  type  of  construction  generally  adopted  for 
large  direct-connected  engine  units. 

When  the  armature  diameter  is  larger  than  30  in.,  so  that  the 
punchings  can  no  longer  be  made  in  one  ring,  the  armature  core 
is  built  up  of  segments  which  are  carried  by  dovetails  on  the 
spider;  the  segments  of  alternate  layers  overlap  one  another  so 
as  to  break  joint  and  give  a  solid  core. 


FIG.  28. — Engine  type  D.-C.  generator. 

The  vent  ducts  in  this  machine  are  obtained  by  setting  strips 
of  sheet  steel  on  edge  as  shown  at  V',  these  strips  are  carried  up 
to  support  the  teeth  and  are  held  in  position  by  projections 
punched  in  the  lamination  adjoining  the  vent  duct.  Vent  ducts 
are  placed  at  the  ends  of  the  core,  partly  for  ventilation  but 
principally  to  support  the  teeth. 

The  poles  are  of  rectangular  cross-section  and  are  built  up  of 
laminations  of  the  shape  shown  at  P.  The  laminations  are 


CONSTRUCTION  OF  MACHINES  29 

0.025  in.  thick  and  are  assembled  so  that  the  cutaway  pole  tips 
of  adjacent  laminations  point  in  opposite  directions.  A  satu- 
rated pole  tip  is  therefore  produced,  which  is  an  aid  to 
commutation.  The  laminations  are  riveted  together  to  form 
a  pole  which  is  then  fastened  to  the  yoke  by  screws. 

The  shaft,  bearings,  and  base  of  such  a  machine  are  generally 
supplied  by  the  engine  builder.  The  bearings  are  similar  to 
those  shown  in  Fig.  27  except  that  the  bushing  is  generally 
made  of  babbitt  metal,  which  is  cast  and  expanded  into  a  cast- 
iron  shell.  One  oil  ring  is  put  in  for  each  8-in.  length  of  the 
bearing  bushing. 

Since  the  shaft  is  supplied  by  the  engine  builder  it  is  necessary 
to  support  the  commutator  from  the  armature  spider,  and  one 
way  of  doing  this  is  shown  in  Fig.  28.  The  brush  rigging  must 
also  be  supported  from  the  machine  in  some  way  and  is  generally 
carried  from  the  yoke  as  shown.  Brushes  of  like  polarity  are 
joined  together  by  copper  rings  R  which  carry  the  total  current 
of  the  machine  to  the  terminals. 

The  yoke  of  a  large  D.-C.  generator  is  always  split  so  that, 
should  the  armature  become  damaged,  the  top  half  of  the  yoke 
can  be  lifted  away  and  repairs  done  without  removing  the 
armature. 


CHAPTER  IV 
INSULATION 

29.  Properties  desired  in  Insulating  Materials. — A  good  in- 
sulator   for    electrical    machinery    must    have    high    dielectric 
strength   and  high  electrical   resistance,   should  be-  tough   and 
flexible,  and  should  not  be  affected  by  heat,  vibration,  or  other 
operating  conditions. 

The  material  is  generally  used  in  sheets  and  its  dielectric 
strength  is  measured  by  placing  a  sheet  of  the  material  0.01  in. 
thick  between  two  flat  circular  electrodes  and  gradually 
raising  the  voltage  between  these  electrodes  until  the  material 
breaks  down.  To  get  consistent  results  the  same  electrodes  and 
'the  same  pressure  between  electrodes  should  be  used  for  all 
comparative  tests;  a  size  of  2  in.  diameter,  with  the  corners 
rounded  to  a  radius  of  0.2  in.,  and  a  pressure  of  1.5  lb.  per  square 
inch,  have  been  found  satisfactory.  The  value  of  the  dielectric 
strength  is  defined  as  the  highest  effective  alternating  voltage 
that  1  mil  will  withstand  for  1  minute  without  breaking  down. 

The  material  should  be  tested  over  the  range  of  temperature 
through  which  it  may  have  to  be  used,  and  all  the  conditions 
of  the  test  and  of  the  material  should  be  noted;  for  example, 
the  dielectric  strength  depends  largely  on  the  amount  of  moisture 
which  the  material  contains  and  is  generally  highest  when  the 
material  has  been  baked  and  the  free  moisture  expelled. 

The  flexibility  is  measured  by  the  number  of  times  the  material 
will  bend  backward  and  forward  through  90  degrees  over  a 
sharp  corner  without  the  fibers  of  the  material  breaking  or  the 
dielectric  strength  becoming  seriously  lessened.  Materials 
which  are  quite  flexible  under  ordinary  conditions  often  become 
brittle  when  baked  so  as  to  expel  moisture. 

30.  Materials  in  General  Use. — For  the  insulation  of  windings 
the    choice    is   limited   to   the   following   materials.     Micanite, 
mica,  varnished  cloth,  paper,  cotton,  various  gums  and  varnishes. 

Cotton  tape  which  is  generally  0.006  in.  thick  and  0.75  in. 
wide  is  put  on  coils  in  the  way  shown  in  Fig.  29,  which  is  called 
half-lap  taping.  Such  a  layer  of  tape  will  withstand  about  250 

30 


INSULATION  31 

volts  when  dry.  When  the  tape  is  impregnated  with  a  suitable 
compound  so  as  to  fill  up  the  air  spaces  between  the  fibers  of 
the  cotton  such  a  half-lap  layer  will  withstand  about  1000 
volts. 

Cotton  Covering. — Small  wires  are  insulated  by  spinning  over 
them  a  number  of  layers  of  cotton  floss;  the  wire  generally  used 
for  armature  and  field  windings  is  insulated  with  two  layers  of 
cotton  and  is  called  double  cotton  covered  (d.c.c.)  wire. 


FIG.  29. — Half -lap  taping. 

Single  cotton-covered  wire  is  sometimes  used  for  field  windings, 
and  for  very  small  wires  silk  is  used  instead  of  cotton  because  it 
can  be  put  on  in  thinner  layers.  The  thickness  of  the  covering 
varies  with  the  size  of  the  wire  which  it  covers,  and  its  value 
may  be  found  from  the  table  on  page  508.  A  double  layer,  with 
a  total  thickness  for  the  two  layers  of  0.007  in.,  will  withstand 
about  150  volts.  When  impregnated  with  a  suitable  compound' 
it  will  withstand  about  600  volts. 

Micanite,  as  used  for  coil  and  commutator  insulation,  is  made 
of  thin  flakes  of  mica  which  are  stuck  together  with  a  flexible 
varnish.  The  resultant  sheet  is  then  baked  while  under  pressure 
to  expel  any  excess  of  varnish  and  is  afterwards  milled  to  a 
standard  thickness,  usually  0.01  or  0.02  in. 

It  is  a  very  reliable  insulator  and,  if  carefully  made,  is  very 
uniform  in  quality.  It  can  be  bent  over  a  sharp  corner  without 
injury  because  the  individual  flakes  of  mica  slide  over  one 
another.  To  make  this  possible  the  varnish  has  to  be  very 
flexible.  Being  easily  bruised,  it  must  be  carefully  handled, 
and  when  put  in  position  on  the  coil,  must  be  protected  by  some 
tougher  material. 

The  dielectric  strength  of  micanite  is  about  800  volts  per  mil 
on  a  10-mil  sample,  and  is  not  seriously  lessened  by  heat  up  to 
150°  C.,  but  long-continued  exposure  to  a  temperature  greater 


32  ELECTRICAL  MACHINE  DESIGN 

than  100°  C.  causes  the  sticking  varnish  to  loose  its  flexibility. 
Micanite  does  not  absorb  moisture  readily,  but  its  dielectric 
strength  is  reduced  by  contact  with  machine  oil. 

Varnished  Cloth. — Cloth  which  has  been  treated  with  varnish  is 
sold  under  different  trade  names.  Empire  cloth  for  example,  is  a 
cambric  cloth  treated  with  linseed  oil.  It  is  very  uniform  in  qual- 
ity, has  a  dielectric  strength  of  about  750  volts  per  mil  on  a  10-mil 
sample,  and  will  bend  over  a  sharp  corner  without  cracking.  It 
must  be  carefully  handled  so  as  to  prevent  the  oil  film,  on  which 
the  dielectric  strength  largely  depends,  from  becoming  cracked 
or  scraped. 

Various  Papers. — These  go  under  different  trade  names,  such  as 
fish 'paper,  rope  paper,  horn  fiber,  leatheroid,  etc.  When  dry, 
they  have  a  dielectric  strength  of  about  250  volts  per  mil  on  a 
10-mil  sample.  They  are  chosen  principally  for  toughness  and, 
after  having  been  baked  long  enough  to  expel  all  moisture,  should 
bend  over  a  sharp  corner  without  cracking.  The  presence  of 
moisture  in  a  paper  greatly  reduces  its  dielectric  strength  and 
generally  increases  its  flexibility;  all  papers  absorb  moisture 
from  the  air.  It  is  good  practice  to  mould  the  paper  to  the 
required  shape  while  it  is  damp,  then  bake  it  to  expel  moisture 
and  impregnate  it  before  it  has  time  to  absorb  moisture  again. 

Impregnating  Compound. — The  compound  which  has  been 
referred  to  is  usually  made  with  an  asphaltum  or  a  paraffin 
base,  which  is  dissolved  in  a  thinning  material.  It  should  have 
as  little  chemical  action  as  possible  on  copper,  iron,  and  in- 
sulating materials.  It  should  be  fluid  when  applied;  must  be 
used  at  temperatures  below  the  break-down  temperature  of  cotton, 
namely  120°  C. ;  should  be  solid  at  all  temperatures  below  100°  C., 
and  should  not  contract  in  changing  from  the  fluid  to  the  solid 
state. 

Elastic  Finishing  Varnish. — This  is  usually  an  air-drying 
varnish  and  is  put  on  the  outside  of  insulated  coils.  It  should 
be  oil-,  water-,  acid-  and  alkali-proof,  should  dry  quickly,  and 
have  a  hard  surface  when  dry. 

31.  Thickness  of  Insulating  Materials. — It  is  not  generally 
advisable  to  use  material  which  is  thicker  than  0.02  in.,  because 
if  there  is  any  flaw  in  the  material  that  flaw  generally  goes  through 
the  whole  thickness,  whereas  if  several  thin  sheets  are  used  the 
flaws  will  rarely  overlap;  thick  sheets  also  are  not  so  flexible 
as  are  thin  sheets.  For  these  reasons  it  is  better  to  use  several 


INSULATION 


33 


layers  of  thin  material  to  give  the  desired  thickness  rather  than 
a  single  layer  of  thick  material. 

32.  Effect  of  Heat  and  Vibration. — It  is  not  advisable  to  allow 
the  temperature  of  the  insulating  materials  mentioned  in  Art.  30 
to  exceed  85°  C.  because,  while  at  that  temperature  the  dielectric 
strength  is  not  much  affected,  long  exposure  to  such  a  temperature 
makes  the  materials  dry  and  brittle  so  that  they  readily  pulverize 
under  vibration.     It  must  be  understood  that  the  final  test  of  an 
insulating  material  is  the  way  it  stands  up  in  service  when 
subjected  to  wide  variations  in  voltage  and  temperature  and 
to  moisture,  vibration,  and  other  operating  conditions  found  in 
practice. 

33.  Grounds  and  Short-circuits. — If  one  of  the  conductors  of 
an  armature  winding  touch  the  core,  the  potential  of  the  core 
becomes  that  of  the  winding  at  the  point  of  contact,  and  if  the 
frame  (yoke,  housings  and  base)   of  the  machine  be  insulated 
from  the  ground,  a  dangerous  difference  of  potential  may  be 


FIG.  30. — Winding  with  grounds. 

established  between  the  frame  and  the  ground.  For  safety 
it  is  advisable  to  ground  the  frame  of  the  machine,  and  then 
the  potential  of  the  winding  at  the  point  of  contact  with  the  core 
will  always  be  the  ground  potential. 

If  the  winding  be  grounded  at  two  points  a  short-circuit  is 
produced  and  a  large  current  flows  through  the  short-circuit, 
this  will  burn  the  windings  before  the  circuit-breakers  can  open 
and  put  the  machine  out  of  operation. 

If,  for  example,  the  winding  shown  in  Fig.  30  becomes  grounded 
at  the  point  a,  the  difference  of  potential  between  the  point 
b  and  the  ground  changes  from  \Et  to  Et,  but  no  short 
circuit  is  produced  unless  there  exists  another  ground  in  the 


34  ELECTRICAL  MACHINE  DESIGN 

winding  at  some  point  d,  or  in  the  system  at  some  point  e.  If 
the  machine  were  a  motor,  a  short-circuit  would  open  the  circuit- 
breakers,  but  not  before  some  damage  had  been  done.  If  the 
machine  were  a  generator,  and  a  short-circuit  took  place  between 
points  a  and  d,the  circuit-breakers  would  not  open  unless  power 
could  come  over  the  line  from  some  other  source,  such  as  another 
generator  operating  in  parallel  with  the  machine  in  question,  or 
from  motors  which  are  driven  as  generators  by  the  inertia  of 
their  load. 

34.  Slot  Insulation  and  Puncture  Test. — As  shown  in  the 
preceding  article,  the  insulation  between  the  conductors  and  a 
core  which  is  grounded  may,  under  certain  circumstances,  be 
subjected  to  a  difference  of  potential  equal  to  the  terminal 
voltage  of  the  machine.  Due  to  operating  causes  still  greater 
differences  of  potential  are  liable  to  occur.  To  make  sure  that 
there  is  enough  insulation  between  the  conductors  and  the  core, 
and  that  this  insulation  has  not  been  damaged  in  handling,  all 
new  machines  are  subjected  to  a  puncture  test  before  they  are 
shipped;  that  is,  a  high  voltage  is  applied  between  the  conductors 
and  the  core  for  1  minute.  If  the  insulation  does  not  break 
down  during  this  test  it  is  assumed  to  be  ample.  The  value  of 
the  puncture  voltage  is  got  from  the  following  table  which  is 
taken  from  the  standardization  rules  of  the  A.  I.  E.  E. 

Rated  terminal  voltage  of  circuit  Rated  output    Testing  voltage 

Not  exceeding  400  volts Under  10  kw 1000  volts 

Not  exceeding  400  volts 10  kw.  and  over. .  .    1500  volts 

400  and  over,  but  less  than  800  volts. . .   Under  10  kw 1500  volts 

400  and  over,  but  less  than   800  volts.. .   10  kw.  and  over. .  .   2000  volts 

800  and  over,  but  less  than  1200  volts. .  .  Any 3500  volts 

1200  and  over,  but  less  than  2500  volts. .  .  Any 5000  volts 

2500  and  over Any Double  nor- 
mal rated 
voltage 

35.  Insulation  of  End  Connections. — Examination  of  Fig.  30 
will  show  that  the  voltage  between  two  end  connections  which 
cross  one  another  may  be,  as  at  point  /,  almost  equal  to  Et}  the 
terminal    voltage.     The    end    connections    must    therefore    be 
insulated  for  this  voltage. 

36.  Surface    Leakage. — If  the    end    connections    had    only 
sufficient  insulation  to  withstand  the  voltage  Et  this  insulation 
would  break  down  during  the  puncture  test  due  to  what  is 


INSULATION 


35 


called  surface  leakage.  Fig.  31  shows  part  of  a  motor  winding 
and  the  insulation  at  the  point  where  the  winding  leaves  the 
slot.  The  slot  insulation  is  sufficient  to  withstand  the  puncture 
test  and  is  continued  beyond  the  slot  for  a  distance  ef.  When 
a  high  voltage  is  applied  between  the  winding  and  the  core  the 
stress  in  the  air  at  b  may  be  sufficient  to  ionize  it,  then  the  air  be- 
tween e  and/ becomes  a  conductor,  the  drop  of  potential  between 
e  and/  becomes  small,  and  the  voltage  across  the  end-connection 
insulation  at  /,  which  equals  the  puncture  voltage  minus  the 


FIG.  31. — Insulation  where  coil  leaves  slot. 

drop  between  e  and  /,  becomes  high.  To  prevent  break-down 
of  the  end-connection  insulation  due  to  this  cause  the  distance 
efis  made  as  large  as  possible  without  increasing  the  'total  length 
of  the  machine  to  an  unreasonable  extent,  and  the  end-connection 
insulation  is  made  strong  enough  to  withstand  the  full  puncture 
voltage  but  with  a  lower  factor  of  safety  than  that  used  for  the 
slot  insulation.  Suitable  values  of  ef,  taken  from  practice,  are 
given  in  the  following  table. 

Rated  terminal  voltage  of  circuit  Length 

Not  exceeding  800  volts 0 . 75  in. 

800  volts  and  over,  but  less  than    2500  volts 1 . 25  in. 

2500  volts  and  over,  but  less  than    5000  volts 2.0    in. 

5000  volts  and  over,  but  less  than    7500  volts 3.0    in. 

7500  volts  and  over,  but  less  than  11000  volts 4.5     in. 

37.  Several  Coil  Sides  in  One  Slot.— In  Fig.  25,  page  21,  is 
shown  part  of  the  winding  diagram  for  a  machine  with  four  coil 
sides  in  each  slot  and  two  turns  per  coil,  and  Fig.  26  shows  a 
section  through  one  of  the  slots  of  the  machine.  This  latter 
figure  is  duplicated  and  shown  in  greater  detail  in  Fig.  34. 

Since  the  voltage  between  two  adjacent  commutator  segments 
seldom  exceeds  20  volts  and  is  more  often  of  the  order  of  5  volts, 


36  ELECTRICAL  MACHINE  DESIGN 

the  amount  of  insulation  between  adjacent  conductors  need  not 
be  large,  thus  the  conductors  shown  are  insulated  from  one 
another  by  one  layer  of  tape  on  each  conductor  and  the  group  of 
conductors  is  then  insulated  more  fully  from  the  core.  The 
completely  insulated  group  of  coils  is  shown  in  Fig.  32,  and 
Fig.  33  shows  the  same  group  of  coils  before  they  are  insulated. 
When  the  individual  coils  are  made  up  of  a  number  of  turns  of 
d.c.c.  round  wire  it  is  advisable  to  put  a  layer  of  paper  between 


FIG.  32.  FIG.  33. 

Coil  for  double  layer  winding  with  two  turns  per  coil  and  8  cond.  per  slot. 

them,  as  shown  at  a,  Fig.  35,  because  the  cotton  covering  may 
become  damaged  when  the  coils  are  squeezed  together  to  get 
them  into  the  slot.  The  voltage  between  adjacent  turns  of  the 
same  coil  is  so  low  that  the  cotton  covering  on  the  conductor 
is  ample  for  insulating  purposes. 

38.  Examples  of  Armature  Insulation. — The  methods  adopted 
in  insulating  coils,  and  the  reasons  for  the  various  operations, 
can  best  be  understood  by  the  detailed  description  of  some  actual 
examples. 

Example  1. — The  insulation  for  the  winding  of  a  240-volt 
D.-C.  generator.  The  winding  is  a  double-layer  multiple  one 


INSULATION  37 

with  two  turns  per  coil  and  four  coil  sides  or  eight  conductors 
per  slot;  the  conductors  are  of  strip  copper  wound  on  edge. 
A  section  through  the  slot  and  insulation  is  shown  in  Fig.  34 
and  the  various  operations  are  as  follows: 

(a)  After  the  copper  has  been  bent  to  shape,  tape  it  all  over 
with  one  layer  of  half-lap  cotton  tape  0.006  in.  thick.  This 
forms  the  insulation  between  adjacent  conductors  in  the  same 
slot. 

(6)  Tape  together  the  two  coils  that  form  one  group  with  one 
layer  of  half-lap  cotton  tape  0.006  in.  thick  all  round  the  coils. 
This  forms  the  end  connection  insulation  and  also  part  of  the 
slot  insulation. 

(c)  Bake  the  coil  in  a  vacuum  tank  at  100°  C.  so  as  to  expel  all 
moisture,  then  dip  it  into  a  tank  of  impregnating  compound 
at  120°  C.  and  leave  it  there  long  enough  to  become  saturated 
with  the  compound. 

(d)  Put  one  turn  of  empire  cloth  0.01  in.  thick  on  the  slot  part 
of  the  coil  and  lap  it  over  as  shown  at  d.     This  empire  cloth 
is  1^  in.  longer  than  the  core  so  that  it  sticks  out  f  in.  from 
each  end. 

(e)  Put  one  turn  of  paper  0.01  in.  thick  on  the  slot  part  of  the 
coil  and  lap  it  over  as  shown  at  e.     This  paper  also  is  1^  in. 
longer  than  the  core;  it  is  not  put  on  for  insulating  purposes  but 
to  protect  the  other  insulation  which  is  liable  otherwise  to  be- 
come damaged  when  the  coils  are  being  placed  in  the  slots. 

(/)  Heat  the  coil  to  100°  C.  and  then  press  the  slot  part  to 
shape  while  hot.  The  heat  softens  the  compound  and  the  press- 
ing forces  out  all  excess  of  compound.  The  coil  is  allowed  to  cool 
while  under  pressure  and  comes  out  of  the  press  with  such  a 
shape  and  size  that  it  slips  easily  into  the  slot. 

(g)  Dip  the  ends  of  the  coil  into  elastic  finishing  varnish. 

Example  2. — The  insulation  for  the  winding  of  a  10  h.p.  500- 
volt  motor  with  a  double  layer  winding  having  five  turns  per 
coil  and  thirty  conductors  per  slot.  The  conductors  are  of  double 
cotton-covered  wire. 

(a)  Put  one  turn  of  paper  0.005  in.  thick  round  the  slot  part 
of  two  of  the  groups  of  conductors  that  form  the  individual  coils. 
This  paper  is  1?  in.  longer  than  the  core  and  forms  part  of  the 
insulation  between  individual  coils  in  the  same  slot  and  also  part 
of  the  insulation  from  winding  to  core. 

(b)  Put  one  turn  of  empire  cloth  0.01  in.  thick  round  the  three 


38 


ELECTRICAL  MACHINE  DESIGN 


coils  that  form  one  group  and  lap  it  over  as  shown  at  6.     This 
empire  cloth  is  1^  in.  longer  than  the  core. 

(c)  Put  one  turn  of  paper  0.005  in.  thick  on  the  slot  part  of  the 
coil,  make  it  also  1^  in.  longer  than  the  core,  and  lap  it  on  the 
top. 

(d)  Tape  the  ends  of  the  group  of  three  coils  with  one  layer 
of  half-lap  cotton  tape  0.006  in.  thick  and  carry  this  tape  on  to 
the  paper  of  the  slot  insulation  for  a  distance  of  i  in.  so  as  to 
seal  the  coil. 

(e)  Wind  the  machine  with  these  coil  groups  putting  a  lining 
of  paper  0.01  in.  thick  in  the  slot  and  a  strip  of  fiber  1/16  in. 
thick  on  the  top  of  the  coils  and  then  hold  the  coils  down  with 
band  wires. 


e  0.01  Paper. 
C?0.01//Empire 
6  H'  Lap  Tape 
a  H  Lap  Tape 


FIG.  34.  FIG.  35. 

Armature  slot  insulation. 


(/)  Place  the  armature  in  a  vacuum  tank  and  bake  it  at 
100°  C.  to  expel  moisture,  then  force  impregnating  compound 
into  the  tank  at  a  pressure  of  60  Ib.  per  square  inch  and  maintain 
this  pressure  for  several  hours  until  the  winding  has  been  thor- 
oughly impregnated. 

(g)  Rotate  the  armature,  while  it  is  still  hot,  at  a  high 
speed  so  as  to  get  rid  of  the  excess  of  compound  which  will 
otherwise  come  out  some  day  when  the  machine  is  carrying 
a  heavy  load. 


INSULATION 


39 


(h)  Paint  the  end  connections  with  elastic  finishing  varnish 
taking  care  to  get  into  all  the  corners. 

39.  Total  Thickness  and  Apparent  Strength  of  Slot  Insulation. — 
Example  1,  Fig.  34. 


Width, 
inches 

Depth, 
inches 

Volts 

Tape  on  conductor 

1,000 

Tape  on  group  of  coils  
Empire  cloth  

0.024 
0  02 

0.024 
0  03 

1,000 
7,500 

Paper    .       .  . 

0  02 

0  03 

2,500 

Total     .... 

0  064 

0  084 

12,000 

In  the  above  table  under  the  heading  of  width  is  given  the 
space  taken  up  in  the  width  of  the  slot  by  the  different  layers 
of  insulation.  The  tape  on  the  conductor  has  not  been  added 
because  it  is  a  variable  quantity  and  depends  on  the  number 
of  conductors  per  slot. 

Under  the  heading  of  depth  is  given  the  space  taken  up  in  the 
depth  of  half  a  slot  by  the  different  layers  of  insulation;  here 
also  the  tape  on  the  individual  conductors  has  not  been  added 
since  it  varies  with  the  number  of  conductors  which  are  vertically 
above  one  another  in  the  slot. 

The  apparent  strength  of  the  above  insulation  is  12,000  volts 
and  the  required  puncture  test  is  1500  volts  so  that  there  is  a 
factor  of  safety  of  8. 

Example  2,  Fig.  35. 


Width, 
inches 

Depth, 
inches 

Volts 

Dec   on  wire 

600 

Paper  on  coils  
Empire  cloth 

0.03 
0  02 

.  0.01 
0  03 

1,250 
7,500 

Paper 

0  01 

0  015 

1,250 

Paper  '.  

0.02 

0.005 

2,500 

Total 

0  08 

0  06 

13,100 

The  puncture  voltage  is  2000  and  the  factor  of  safety  =6.5. 


40 


ELECTRICAL  MACHINE  DESIGN 


-2  Layers  O.Ol"Paper. 

-  Via  Cardboard. 

-2  Layers  0.006"Tape. 


0.006  Tape. 
0.03  "Paper. 
0.03"Canvas. 
0.025"Steel. 


0.03"Canvas. 


FIG.  36. — Field  coil  insulation. 


/Tape 


Wood 


FIG.  37. — Ventilated  field  coils. 


INSULATION  41 

40.  Field  Coil  Insulation. — Two  examples  of  field  coil  insula- 
tion are  shown  in  Fig.  36.  Diagram  A  shows  an  example  of  a 
coil  which  is  carried  in  a  cardboard  spool  while  diagram  B  shows 
an  example  of  a  coil  which  is  carried  in  an  insulated  metal  spool. 
In  both  cases  the  coils,  after  being  wound  in  the  spool  and  taped 
up,  are  baked  in  a  vacuum  and  then  impregnated  with  compound. 
This  compound  is  a  better  insulator  than  the  air  which  it  replaces 
it  is  also  a  better  conductor  of  heat. 

Figure  37  shows  the  type  of  coil  which  is  used  to  a  large  extent 
on  machines  the  armature  diameter  of  which  is  greater  than  20 
in.  The  shunt  coils  are  made  of  d.c.c.  wire,  wound  in  layers; 
the  individual  shunt  coils  are  1  in.  thick  and  are  separated  by 
ventilating  spaces  1/2  in.  wide.  The  insulation  is  carried  out 
entirely  by  wooden  spacing  blocks  so  that  there  is  a  large  radi- 
ating surface,  and  also  little  insulation  to  keep  in  the  heat. 
The  coils  are  made  self-supporting  by  being  impregnated  with  a 
solid  compound  at  about  120°  C. 

The  insulation  on  the  individual  turns  of  the  series  coil  con- 
sists of  one  layer  of  cotton  tape  0.006  in.  .thick  and  half  lapped; 
this  coil,  when  made  of  strip  copper  as  shown,  is  not  impregnated 
but  is  dipped  in  finishing  varnish. 


CHAPTER   V 
THE  MAGNETIC   CIRCUIT 

41.  The  Magnetic  Path. — Fig.  38  shows  two  poles  of  a  multi- 
polar  D.-C.  generator,  each  pole  of  which  has  an  exciting  coil  of 
Tf  turns  through  which  a  current  //  flows.  Due  to  this  excita- 
tion a  magnetic  flux  is  produced  and  the  mean  path  of  this  flux 
is  shown  by  the  dotted  lines.  This  magnetic  flux  consists  of 
two  parts,  one,  <j)a,  which  crosses  the  air  gap  and  is  therefore  cut 
by  the  armature  conductors,  and  the  other,  (f>e,  which  does  not 
cross  the  air  gap  and  is  called  the  leakage  flux. 


FIG.  38. — The  paths  of  the~main  and  of  the  leakage  fluxes. 

42.  The  Leakage  Factor. — The  total  flux  which  passes  through 
the  yoke  and  enters  the  pole  =  <£m  =  <£a  +  <£<?  and  the  ratio  -£—  is 

called  the  leakage  factor  and  is  greater  than  1. 

43.  The  Magnetic  Areas. — The  meanings  of  the  symbols  used 
in  this  article  will  be  understood  by  reference  to  Fig.  38. 

Da    =  the  external  diameter  of  the  armature. 
p      =  the  number  of  poles. 

T      =  the  pole  pitch  = — -• 

pole  arc 


=  the  per  cent,  enclosure  of  the  pole  =  — ? — nft~h' 

=  the  axial  length  of  the  armature  core. 

42 


THE^MAGNETIC  CIRCUIT  43 

m     ~  the  number  of  vent  ducts  in  the  center  of  the  core. 

v       =  the  width  of  each  vent  duct. 

Lg    =  the  gross  length  of  the  iron  in  the  core  =Lc  —  mv. 

Ln    =  the  net  length  of  the  iron  in  the  core  =0.9  Lg]  it  is  less 

than  Lg   by   the   amount    of   the  insulation  between 

laminations. 

./V     =  the  total  number  of  slots  in  the  armature. 
^       =  the  slot  pitch, 
s       =  the  slot  width. 
t       =  the  tooth  width. 
d      =  the  depth  of  the  slot. 

da     =  the  depth  of  the  armature  core  below  the  slot. 
W  p  =  the  pole  waist. 
Lp    =  the  axial  length  of  the  pole. 
Then: 
Ag    =  the  apparent  gap  area  per  pole  =</>rLc. 

Aag  =  the  actual  gap  area  per  pole  =-^r  where  C  is  a  constant 

greater  than  1,  called  the  Carter  coefficient.  This 
constant  takes  into  account  the  effect  of  the  slots  in 
reducing  the  air-gap  area. 

N 
At    =  the  tooth    area   per   pole     =</> — tLn;  only  those  teeth 

which  are  under  the  poles  are  effective. 
Ac    =  the  area  of  the  armature  core  =daLn. 
Ap  =  the  pole  area   =WPLP  when  the  pole  is  solid;   when 
built   up   of   laminations   the   pole   area    =(WPLPX 
const.)    where   the    const,    is    a   stacking   factor    and 
=  0.95  approximately: 
Ay   =  the  yoke  area. 

44.  The  Carter  Coefficient. l— Fig.  39  shows  the  path  of  the 
magnetic  flux  across  the  air  gap.  If  it  were  not  for  the  armature 
slots  and  vent  ducts  the  air-gap  area  per  pole  would  be  ^rl/c 
which  is  called  the  apparent  gap  area.  The  actual  gap  area  per 

(T*  \  Ji 

-,<prLc  }  where  -»  Fig.  39,  is  the  Carter  coefficient. 

x  =  t+fs  where/  depends  on  the  slot  width  s  and  on  the  air- 
gap  thickness  d,  and  is  got  from  Fig.  40  for  different  values  of  the 

ratio  ^ •  then  C.  the  Carter  coefficient  =  -  =  rT7~* 

d '  x     t  +/s 

lElec.  World  and  Engineer,  Nov.  30,  1901. 


44 


ELECTRICAL  MACHINE  DESIGN 


FIG.  39. — Distribution  of  flux  in  the  air-gap. 


1.0 

^~ 

s 

\ 

1 

1 

1 

O.o 

\ 

k 

J 

\ 

<-i- 

3 

—  s-> 

u 

rf 

\ 

X 

H 

«t-+ 

-fs-> 

f 

_ 

^*v 

1 

^^ 

»^^ 

2 

^^^_ 

/  + 

fs 

"^*"111^- 

"*^, 

-^ 

**•    ^ 

—    — 

•~  ^. 

^== 

Values  of  -f- 
n 


FIG.  40. — The  Carter  fringing  constant. 


ISGsq.in.    ' 


Slots   200-0.43  xl.6 
Coils   400 
Winding       1  Turn 

Mult. 
Z.  800 

Poles     10      ' 
K.W.     400 
Volts    no  load     240 
Volts  full  load    240 
.R.P.M.     200 


FIG.  41. — Magnetic  circuit. 


THE  MAGNETIC  CIRCUIT  45 

It  is  required  to  find  the  value  of  the  Carter  coefficient  for  the  machine 
drawn  to  scale  in  Fig.  41. 
s  =0.43  in. 
/  -0.48  in. 
8  =0.3  in. 

1-1.44 

/  =0.78  from  Fig.  40 

=0.48  +  0.43 

0.48  +  0.78X0.43 

There  is  a  small  amount  of  fringing  at  the  pole  tips  which 
tends  to  increase  the  air-gap  area,  but  its  effect  is  counter- 
balanced by  the  fact  that  at  the  pole  tips,  d,  the  thickness  of  the 
air  gap,  is  increased. 

.  The  Carter  coefficient  for  the  vent  ducts  can  be  found  in  the 
same  way  as  for  the  slots,  but  since  its  value  is  nearly  always  =  1 
the  calculation  is  seldom  made. 

45.  The  Flux  Densities. — The  flux  in  the  different  parts  of  the 
magnetic  circuit  is  shown  in  Fig.  38,  then: 

Bg   =  the  apparent  flux  density  in  the  air  gap  =  ^- 

AQ 
Bag=  the  actual  flux  density  in  the  air  g&p  =  CBg. 

Bt    =  the  apparent  flux  density  in  the  teeth  =  ^- 

At 

Bc    =  the  flux  density  in  the  armature  core^T^-- 

ZAC 

Bp  =  the  flux  density  in  the  pole  =  -^- 

Ap 

By  =  the  flux  density  in  the  yoke  =  ^j 

ZAy 

The  flux  density  in  the  teeth  at  normal  voltage  is  generally 
about  150,000  lines  per  square  inch,  and  at  such  densities  the 
permeability  of  the  iron  in  the  teeth  becomes  comparable  with 
that  of  air,  so  that  a  considerable  amount  of  flux  passes  down  the 
slots,  vent  ducts,  and  the  air  spaces  between  the  laminations. 
.If  the  assumption  is  made  that  the  teeth  have  no  taper,  and  that 
the  lines  of  force  are  parallel  both  in  the  teeth  and  in  the  air 
paths,  and  if 

Bat=  the  actual  flux  density  in  the  teeth, 

Bs  =  the  flux  density  in  the  air  path  consisting  of  the  slots, 
vent  ducts,  and  air  spaces  between  laminations, 

B't   =  the  apparent  flux  density  in  the  teeth,  then 


46  ELECTRICAL  MACHINE  DESIGN 

<j)a  =  the  total  flux  per  pole  entering  the  armature  =  BtAt, 
=  BatAi  +  BsAs,  where  A8  is  the  area  of  the  air  path  per 
pole;  therefore 


For  a  given  number  of  ampere-turns  between  the  two  ends  of  the 

slot,  assuming  the  slot  to  be  1  in.  deep, 

Bs   =  3.2  (ampere-turns);  formula  1,  page  6. 

Bat=  the   value   of   flux   density   corresponding   to   the   given 

number  of  ampere  turns,  found  from  Fig.  42. 
Bt,  corresponding  to  the  given  number  of  ampere-turns,  is  found 
by  substitution  in  the  above  formula. 

The  relation  between  Bt  and  Bat  is  plotted  in  Fig.  43  for 

different  values  of  the  ratio  -  and  for  the  magnetization  curve 

in  Fig.  42,  the  assumption  being  made  that  Ln  =  O.S  Lg.  For 
example,  suppose  that  in  a  particular  case  the  width  of  tooth  is 

equal  to  that  of  the  slot  so  that  i  =  2,  that  the  ratio  ~  =  0 .  8 , 

t  J^c 

and  that  the  actual  flux  density  in  the  tooth  is  160,000  lines  per 
square  inch.  Then  the  ampere-turns  necessary  to  send  this 
flux  through  1  in.  of  the  tooth  is  2250,  from  Fig.  42;  the  flux 
density  in  the  air  path  due  to  2250  ampere-turns  is  3.2X2250  = 
7200  lines  per  square  inch,  see  formula  1,  page  6,  and 

5^=160,000  +  7200  (^o'.8*)  where /I  =  2* 

'  \    O.ot    I 

=  170,800  lines  per  square  inch. 
46.  Calculation    of    the    No-load    Saturation    Curve. — It    is 

required  to  find  the  number  of  ampere-turns  necessary  to  send  a 
certain  flux  <j>a  across  the  air  gap  of  the  machine  shown  in  Fig. 
38. 

The  m.m.f.  between  points  a  and  b  is  Tflf  ampere-turns  and 
this  must  be  equal  to  ATy  +  ATp  +  ATg  +  ATt  +  ATC,  where 

ATy  is  the  ampere-turns  necessary  to  send  the  flux  %(j>m 
through  the  length  ly  of  the  yoke.  The  value  of  By  is  known 
and  the  corresponding  number  of  ampere-turns  required  for 
each  inch  of  the  yoke  path  is  found  from  Fig.  42.  This  value  of 
ampere-turns  per  inch  multiplied  by  the  length  ly  gives  the  value 
of  ATu. 


THE  MAGNETIC  CIRCUIT 


47 


170  x  103 


S"g 

j^t* 

.x-^ 

-  8 

I?1"!      i«n 

x-*1 

-** 

a  d"    16° 

3  w 

^x- 

--* 

m    ^ 

x^ 

x 

Q  a      150 

X   m 

^ 

^CJ 

x^ 

g  g 
EC      -MA 

^ 

^ 

^ 

*^^ 

75 

^ 

iX^* 

i 

x"* 

^ 

CQ  130 

** 

,^ 

J190 

/ 

CO 

/ 

'•K. 

0 

OL 

0 

S( 

K) 

10 

JO 

VI 

00 

14 

00 

1G 

JO 

ISi 

>0 

20 

W) 

22 

00 

24 

00 

2tt 

DO 

§110 

-..  / 

2( 

/ 

xT 

mr 

er 

3  1 

uri 

1ST 
^—  - 

or 

^,.1^ 

111 

^ 

ch 

^^> 
--• 

fin  **  ion 

^w 

et 

b^ 

e^V 

*^* 

^^« 
.-*-• 

^*** 

•••i"" 

«^" 

^. 

^-> 

.  — 

TO 

^ 

\ 

^ 

en  r*S      on 

/ 

' 

x 

*"   ( 

>fc 

^  —  • 

^-^ 

/ 

/ 

r^ 

0^ 

,^ 

**** 

** 

2  4Q           go 

I/ 

f 

c 

>*b 

.  — 

1 

/ 

^ 

•^ 

3 

ri  10          70 

1 

/ 

•^ 

/ 

20          fiO 

/ 

\ 

y 

I 

10        50 

20      40      60       80     100     120     140     160     180    200 
Ampere  Turns  per  Inch 

FIG.  42. — Magnetization  curves. 


170  xlO3 


160 


150 


.5  140 
^c 
.-S  130 


120 


110 


4=2 

__=2.5 
_=3 


110         120         130          140         150         160         170        180*  10 3 
Apparent  Density  in  Lines  per  Sq  Jn. 

FIG.  43. — Densities  in  armature  teeth. 


48 


ELECTRICAL  MACHINE  DESIGN 


ATP  is  the  ampere-turns  necessary  to  send  the  flux  (f>m 
through  the  length  lp  of  the  pole  and  is  found  in  a  similar  manner. 

AT 'g  is  the  ampere-turns  necessary  to  send  the  flux  c/>a  across 
one  air  gap.  To  find  this  value  it  is  necessary  to  find  first  of  all 
the  value  of  C,  the  Carter  coefficient,  and  then  the  actual  flux 
density  in  the  air  gap,  namely  Bag  —  CBg. 

AT 

Bag  lines   per  square   inch  =3. 2  — r-^  (3) 

where  d  is  the  air  gap  thickness  in  inches. 

ATt  is  the  ampere-turns  necessary  to  send  the  flux  (j>a  through 
the  length  d  of  the  tooth.  The  value  of  Bt,  the  apparent  tooth 


160xlO 


70 


20    40    60    80    100   120   140   160   180   200 

Amoere  Turns  per  In. 
FIG.  44. — Magnetization  curves  for  sheet  steel. 


density,  is  readily  found,  and  the  value  of  Bat,  the  actual  flux 
density,  can  be  found  by  the  use  of  the  curves  in  Fig.  43.  The 
value  of  ampere-turns  per  inch  corresponding  to  this  actual  density 
can  then  be  taken  from  Fig.  42.  This  latter  quantity  when 
multiplied  by  d  gives  the  value  of  ATt. 

When  the  teeth  are  tapered  as  shown  in  Fig.  44,  so  that  the 
flux  density  is  not  uniform  through  the  total  depth  of  the  tooth, 


THE  MAGNETIC  CIRCUIT  49 

the  problem  becomes  more  difficult.  It  is  necessary  to  divide 
the  tooth  length  d  into  a  number  of  small  parts,  find  the  average 
flux  density  in  each  of  these  parts  and  the  corresponding  value 
of  ampere-turns  per  inch;  the  average  value  of  these  latter 
quantities  multiplied  by  d  gives  the  value  of  ATt.  This  process 
is  slow,  but  in  Fig.  44  is  plotted  a  series  of  curves  whereby,  if  the 
actual  flux  density  at  the  top  and  bottom  of  the  tooth  is  known, 
the  average  ampere-turns  per  inch  can  be  found  directly. 

ATC  is  the  ampere-turns  necessary  to  send  the  flux  J<£a 
through  the  length  lc  of  the  core  and  is  found  by  the  use  of  the 
curves  in  Fig.  42. 

Example.  —  Fig.  41  shows  a  dimensioned  sketch  of  a  10-pole,  400-kw.,  240- 
volt,  200  r.  p.  m.  generator;  it  is  required  to  draw  the  no-load  saturation 
curve  for  this  machine. 

r.p.m.  poles  ., 
=  ^ 


240X60X10X108 
therefore  <£a  =  800x2()()xio 

=  9X  106  at  240  volts,  no-load. 
The  magnetic  areas: 
r      =  the  pole  pitch  =  —^—  =  18.2  in. 

0      =  the  per  cent,  enclosure  =0.7. 

Lg    =  the  gross  iron  =10.5  in. 

LB    =the  net  iron  =9.45  in. 

\      =the  slot  pitch  =0.91  in.  at  top  of  slot. 

=  0.86  in.  at  bottom  of  slot. 
/       =the  tooth  width  =0.48  in.  at  top. 

=  0.43  in.  at  bottom. 

Ag   =  the  apparent  gap  area  =0.7X  18.2X  12  =  153  sq.  in. 

C      =the  Carter  coefficient  =1.12  from  Art.  44,  page  45. 

200 
At    =  the  minimum  tooth  area  per  pole    =  0.  7  Xy~-X  0.43X9.45 

=  57  sq.  in. 

Ac    =the  core  area  =5.65X9.45  =  53.5  sq.  in. 

Ap   =the  pole  area  =0.95X  10.5X  11.5  =  114  sq.  in. 

Ay   =the  yoke  area  =136  sq.  in. 

The  flux  per  pole: 

<£0    =the  useful  flux  per  pole  =9X  10°. 

If      =  the  leakage  factor  =1.16,  see  page  53. 

0m  =the  total  flux  per  pole  =  10.5  X  106. 

The  flux  densities: 

Bff    =  the  apparent  gap  density  =59,000  lines  per  sq.  in. 

Bt    =  the  apparent  tooth  density  =158,000  lines  per  sq.  in. 

Bat  =the  actual  tooth  density  =150,000  lines  per  sq.  in.,  from 

Fig.  43. 


50 


ELECTRICAL  MACHINE  DESIGN 


Bc    =the  core  density 
Bp   =  the  pole  density 
By    =  the  yoke  density 
The  excitation: 


=  84,000  lines  per  sq.  in. 
=  93,000  lines  per  sq.  in. 
=  39,000  lines  per  sq.  in. 


gap    ampere-turns    = 


1.12X59,000X0.3 
3.2 


=  6200 


ATt    =  the  tooth  ampere- turns  =  1300 XI. 6  =2080 

Use  curves  in  Fig.  44  with  a  tooth  taper  of  1.12  and  a  flux  density  of 

150,000  lines  per  sq.  in. 

ATC   =  th«  core  ampere-turns   =20X6.5  =    130 

ATP  =  the  pole  ampere- turns   =40X15  =   600 

ATy  =  the  yoke  ampere- turns  =  75X13  =  980 

Total  ampere- turns  for  240  volts  at  no-load  =9990 


280 


240 


200 


I 

1 160 

I 
120 


80 


40 


A 


46  8  10 

Ampere  Turns  per  Pole 

FIG.  45. — No-load  saturation  curve. 


12 


14xl03 


In  the  above  calculation  two  factors  have  been  omitted  which 
would  cause  the  excitation  to  be  slightly  larger  than  that  cal- 
culated, namely,  the  excitation  required  to  send  the  flux  across 
the  joint  between  the  pole  and  the  yoke,  and  also  the  extra 
excitation  required  for  the  yoke  due  to  the  fact  that,  near  the 


THE  MAGNETIC  CIRCUIT 


51 


contact  surface  between  the  pole  and  the  yoke,  the  yoke  density 
is  high,  being  equal  to  that  of  the  pole. 

Two  other  points  at  different  voltages  are  figured  out  and  the 
results  are  tabulated  as  shown  in  the  following  table. 


No-load  voltage  
Flux  per  pole  
Leakage  factor  

240 
9X106 
1.16 

280 
10.5  X106 
1.16 

210 
7.9  X106 
1.16 

. 

Length 

Area 

Density 

AT 

Density 

AT 

Density 

AT 

Air  gap  
Min.  tooth  
Core  

0.30 
1.60 

6.5 
15.0 
13.0 

153 

ri2 

57 

53.5 
114 
136 

59,000 

158,000 
150,000 
84,000 
93,000 
39,000 

6200 

2080 
130 
600 
980 

184,000 
170,000 
98,000 
108,000 
45,000 

7200 

3400 
450 
2400 
1460 

138,000 
134,000 
73,000 
81,000 
34,000 

5400 

1200 
78 
270 
.    680 

Pole  
Yoke  

Total  amp.  -turns  per  pole  

9990 

14950 

7628 

From  these  figures  the  no-load  saturation  curve  in  Fig.  45  is 
plotted. 

47.  Calculation  of  the  Leakage  Factor.  —  Fig.  46  shows  part  of 
a  machine  which  has  a  large  number  of  poles.  The  total  leakage 
flux  per  pole  =(f>e  =  <l>ei  +  <l>e2  +  <l>e3  +  </>e4,  where 

(j>ei=  the  leakage  flux  in  paths  1,  between  the  inner  faces  of 

the  pole  shoes. 
(j)62=  the  leakage  flux  in  paths  2,  between  the  flanks  of  the 

pole  shoes. 
0es  =  the  leakage  flux  in  paths  3,  between  the  inner  faces  of  the 

poles. 
<fie4=  the  leakage  flux  in  paths  4,  between  the  flanks  of  the 

poles. 
The  m.m.f.  across  paths  1  and  2  =  2(ATa  +  ATt  +  ATc) 

=  2(ATg+t),  since  ATC  can  be 
neglected;  therefore,  the  flux  across  one  path  1 

=  3.2  x2(ATg+t)I~^  from  formula  1,  page  6; 


and 


—  r-  ^  since  there  are  two  paths  1,  per  pole. 


52 


ELECTRICAL  MACHINE  DESIGN 


The  flux  across  one  path  2  =  3.2x2(AT0+i)     |     My 


/Ws 
\A 
hsdy 
L  +  ny 
_ 


Yok 

e 

—  - 

> 

f 

<—  "is—  > 

.-"' 

VN-~ 

.-a).— 

-"I 

h 

•s^ 

ZH—  ^i-H_ 

F--Ci>—  I 

1 

— "0 — 


FIG.  46. — The  leakage  paths. 


and  (f)e2  =  l9(ATg+t)hs  Iog10 


1-4—  - 

l 

1 

1 

l 

1 

1 

1 

1 

1 

I 

/ 

I 
\ 

since  there  are  four  paths 


2,  per  pole. 

The  m.m.f.  across  the  paths  3  and  4  varies  from  zero  at  the 
bottom  of  the  poles  to  2(ATg+t)  at  the  shoe,  and  the  average 
value  is  taken  as  ATg+t  ampere-turns,  so  that 


and 


THE  MAGNETIC  CIRCUIT  53 

Given  the  complete  data  on  a  magnetic  circuit,  the  value  of 
ATg+t,  the  ampere-turns  to  send  the  flux  <j)a  across  one  gap  and 
tooth,  can  be  found,  and  then  the  value  of  <j>e  =  <pei  +  <f>ez  +  <£e3  + 
(f>e±  can  be  obtained  by  substitution  in  the  above  formulae. 

The  leakage  f actor  =  r^p^- 

9a 
It  is  required  to  find  the  leakage  factor  for  the  machine  shown  in  Fig.  41. 


h8 

=  1.5  in. 

L8 

=  11.5  in. 

ifj 

=  6  in. 

W8 

=  12.7  in. 

hp 

=  13.5  in. 

Lp 

=  11.  5  in. 

=  12.5  in. 

Wp 

=  10.5  in. 

then  <f>ei 

i*rir  ^    /L5xll-5\ 

-37(4r,+() 

10  (/!../  g+t)         \              Q             / 

*, 

"1  Q  f  A  rji      i   A    1     £>  lr\rr          /'IL                    "      1 

-18(4^+,) 

—  iy^Yi.f  fir+<y  J--<-'  1(->&io    V1  >      ox/«     J 
^  X  O    / 

A-. 

^VAT.^     /13.5X11.6\ 

RO(AT~,A 

v    ,  ,-      7rXl0.5\ 

,)   13.5  tog,.  (1+^1^5) 

and  <j)e   =  the  total  leakage  flux  per  pole  =18l(ATg+t) 

The  value  of  ATg+t  from  the  table  on  page  51. 
=  6200  +  2080 
=  8280  ampere  turns 
therefore  <j>e  =  181 X  8280 
=  1,500,000 
and  <j>a  the  flux  per  pole  which  crosses  the  gap 

=  9. OX  106  from  the  table  on  page  51 ; 

therefore  the  leakage  f  actor  =. 

_  9,000,000 +  1,500,000 

9,000,000 
=  1.16 

For  a  first  approximation  the  following  values  of  the  leakage 
factor  may  be  used: 

Four-pole  machines  up  to  10-in.  armature  diameter  1.25 

Multipolar  machines  between  10  and  30-in.  diameter         1.2 

between  30  and  60-in.  diameter          1.18 

greater  than  60-in.  diameter  1.15 

These  values  apply  to  the  type  of  machine  shown  in  Fig.  28. 


CHAPTER  VI 
ARMATURE  REACTION 

48.  Armature  Reaction.  —  In  Fig.  47,  A  shows  the  magnetic 
field  that  is  produced  in  the  air  gap  of  a  two-pole  machine  by 
the  m.m.f.  of  the  main  exciting  coils. 


x    y 


Distribution  of  Flux  due  to 
m.m.f .  of  Main_Field. 


Distribution  of  Flux  due  to 
m.m.f.  of  Armature. 

D 


Distribution  of  Flux 
uirder  Load  Conditions. 

FIG.  47. — Flux  distribution  curves. 


B  shows  the  armature  carrying  current    and   the   magnetic 
field  produced  thereby    when  the  brushes  are  in  the  neutral 

54 


ARMATURE  REACTION  55 

position  and  the  main  field  is  not  excited.  The  m.m.f.  between 
a  and  b,  called  the  cross-magnetizing  ampere-turns  per  pair  of 
poles,  due  to  the  current  Ic  in  each  of  the  Z  conductors  =  J  ZIC 
ampere-turns,  and  that  between  c  and  d  and  also  that  between  g 
and  h  =  $  <f>ZIc  ampere-turns.  Half  of  this  latter  m.m.f.  acts 
across  the  path  ce  and  the  other  half  across  the  path  fd  since  the 
reluctances  of  the  paths  ef  and  cd  are  so  low  that  they  may  be 

neglected.     Therefore,  the  cross-magnetizing  effect  at  each  pole 
17 

tip  =  J  </>—Ic  for  any  number  of  poles  (4) 

C  shows  the  resultant  magnetic  field  when,  as  under  operating 
conditions,  both  the  main  and  the  armature  m.m.fs.  exist  to- 
gether. The  flux  density,  compared  with  the  value  shown  at  A, 
is  increased  at  the  pole  tips  d  and  g  and  decreased  at  the  pole  tips 
c  and  h. 

A  convenient  method  of  showing  the  flux  distribution  in  the 
air  gap  is  shown  in  diagrams  D,  E  and  F,  Fig.  47,  which  are 
obtained  by  assuming  that  the  diagrams  A}  B  and  C  are  split 
at  xy  and  opened  out  on  to  a  plane,  and  that  the  flux  density  at 
the  different  points  is  plotted  vertically. 

D  shows  the  flux  distribution  due  to  the  main  m.m.f.  acting 
alone. 

E  shows  the  flux  distribution  due  to  the  armature  m.m.f. 
acting  alone. 

F  shows  the  resultant  distribution  when  both  the  main  and  the 
armature  m.m.fs.  exist  together  and  is  obtained  by  adding 
the  ordinates  of  curves  D  and  E.  It  is  permissible  to  add  these 
ordinates  of  flux  density  together  provided  that  the  paths  df  and 
gk  do  not  in  the  meantime  become  highly  saturated.  These 
paths,  however,  include  the  gap  and  teeth,  and  the  flux  density 
in  the  teeth  due  to  the  main  field  is  about  150,000  lines  per 
square  inch  at  normal  voltage,  which  is  well  above  the  point  of 
saturation,  so  that  an  increase  in  m.m.f.,  such  as  that  at  /  due 
to  the  armature  m.m.f.,  will  produce  an  increase  in  flux  density  at 
pole  tip/  of  only  a  small  amount;  while  a  decrease  in  m.m.f.  of 
the  same  value  at  pole  tip  e  will  produce  a  decrease  in  flux  density 
at  that  pole  tip  of  a  much  larger  amount;  thus  the  total  flux  per 
pole  will  be  decreased. 

It  is  usual  to  consider  the  effect  of  armature  reaction  as  being 
due  to  a  number  of  lines  of  force  acting  in  the  direction  shown 
in  diagram  B,  Fig.  47,  and  this  diagram  shows  that  the  same 


56 


ELECTRICAL  MACHINE  DESIGN 


number  of  lines  is  added  at  the  one  pole  tip  as  is  subtracted  at  the 
other  pole  tip.  A  truer  representation  is  that  shown  in  Fig.  48. 
Since  the  lines  of  force  of  armature  reaction  meet  a  high  reluc- 
tance at  d  some  of  them  take  the  easier  path  through  hmc. 
These  latter  lines  are  in  the  opposite  direction  to  those  of  the 
main  field  and  are,  therefore,  demagnetizing. 


FIG.  48. — Demagnetizing  effect  of  armature  reaction  with  the  brushes  at 

the  neutral  point. 

49.  Distribution  of  Flux  in  the  Air  Gap  at  Full  Load.1— Fig.  49 
is  part  of  the  development  of  a  multipolar  machine  with  p  poles, 
and  curve  D  shows  the  flux  distribution  in  the  air  gap  due  to  the 
main  m.m.f.  acting  alone.  The  armature  m.m.fs.  across  df  and 

17 

ce  each  =  J  ^—  Ic  ampere-turns  and  curve  G  shows  the  distribu- 
tion of  the  armature  m.m.f. 

Curve  1,  Fig.  50,  is  the  no-load  saturation  curve  of  the  machine 

and  curve  2  is  that  part  of  this  saturation  curve  for  the  tooth, 

gap  and  pole  face,  so  that  if  oy  is  the  ampere-turns  per  pole 

required  to  send  the  no-load  flux  through  the  magnetic  circuit 

of  the  machine  then  ox  is  that  necessary  to  send  this  same  flux 

through  the  length  of  one  gap,  one  tooth  and  one  pol  eface. 

Across  np,  Fig.  49,  the  m.m.f.  at  full-load  is  the  same  as  at 

1  The  method  adopted  in  this  article  is  a  slight  modification  of  that  pro 

posed  by  S.  P.  Thompson,  Chapter  XVII,  Dynamo  Electric  Machinery,  Vol.  I. 


ARMATURE  REACTION 


57 


FIG.  49. — Flux  distribution  at  full-load. 


Flux  per  Pole 


Ampere  Turns  per  Pole 


FIG.  50. — No-load  saturation  curves. 


58 


ELECTRICAL  MACHINE  DESIGN 


no-load  and  therefore  the  flux  density  in  the  air  gap  at  n  is 
unchanged. 

Across  df  the  m.m.f.  at  full-load  is  no  longer  ox,  Fig.  50,  but 

2 
=  oxl,    where    xxl  =  ^  —  7c  =  the  m.m.f.    across  df  due  to  the 

armature;   therefore   the    flux    density  in   the  air  gap  at  d  at 

full-load  is  increased  over  its  value  at  no-load  in  the  ratio  ^— *-j 

sx 

Fig.  50,  and  is  so  plotted  at  dw,  Fig.  49. 

Across  ce  the  m.m.f.  at  full-load  is  no  longer  ox,  Fig.  50,  but 

Z 
—  ox2,    where    xx2~%<{>  —Ic,  and  therefore  the  flux  density  in 

the  air  gap  at  c  at  full-load  is  less  than  that  at  no-load  in  the 

'ijnf* 

ratio  — -;  Fig.  50,  and  is  so  plotted  at  cz,  Fig.  49. 
sx 

Thus,  in  Fig.  49,  curve  D  shows  the  distribution  of  the  flux  in 
the  air  gap  at  no-load  and  curve  F  that  at  full-load.  The  total 
flux  per  pole  is  less  at  full-load  than  at  no-load  in  the  ratio  of  the 
area  enclosed  by  curve  F  to  that  enclosed  by  curve  D,  which 

ratio  is  practically  the  same  as  area    2  ;•  1>  Fig.  50. 


Y 

FIG.  51.  FIG.  52. 

Demagnetizing  and  cross  magnetizing  effect  of  the  armature. 

50.  Armature  Reaction  when  the  Brushes  are  Shifted. — Fig.  51 
shows  the  armature  carrying  current  and  the  magnetic  field 
produced  thereby  when  the  brushes  are  shifted  through  an 
angle  0  so  as  to  improve  the  commutation.  The  armature 
field  is  no  longer  at  right  angles  to  the  main  field  and  the  easiest 
way  in  which  to  consider  its  effect  is  to  assume  that  it  is  the 
resultant  of  two  components,  one  in  the  direction  OY  which  is 


ARMATURE  REACTION  59 

called  the  cross-magnetizing  component,  the  effect  of  which  has 
already  been  discussed,  and  another  in  the  direction  OX  which 
is  called  the  demagnetizing  component  because  it  is  directly 
opposed  to  the  main  field.  Fig.  52  shows  the  armature  divided 
up  so  as  to  produce  these  two  components,  and  it  will  be  seen 
that  the  demagnetizing  ampere-turns  per  pair  of  poles 


or  the  demagnetizing  ampere-turns  per  pole 

iz  2d 

:V  180 

The  angle  6  for  preliminary  calculations  is  usually  taken  as  18 

26 
electrical  degrees  so  that  ^7,  =  0.2. 

loU 

51.  The  Full  Load  Saturation  Curve.  —  It  is  required  to  draw 
this  curve  for  the  machine  which  is  drawn  to  scale  in  Fig.  41 
and  to  which  the  following  data  applies. 

Rating:    400  kw.,  240  volts,  1670  amp.,  200  r.p.m. 

Poles  ............................................  10 

Coils  ............................................  400 

Winding  ...............................    .  .  one  turn  multiple 

Total  conductors  .................................  800 

Current  per  conductor  .............................  167 

Per  cent,  pole  enclosure  ............................  0.7 

Volts  drop  at  full-load  across  armature,  brushes  and 

series  field  .....................................  8.7 

6,  the  angle  of  advance  of  the  brushes  ...............  18  degrees 

800X167 
Armature  ampere-  turns  per  pole  =  —  -  ^   ..........  6700 

2i    X    10 

(800 
—  -  X  0  .  2  X  167)  =  1340 

(800 
-jQ-  X0.7  X  167)  =4700 

Curve  1,  Fig.  53,  the  no-load  saturation  curve,  is  taken  directly 
from  Fig.  45. 

Curve  2,  Fig.  53,  that  part  of  the  saturation  curve  for  the  tooth 
and  gap,  is  plotted  from  the  figures  in  the  table  on  page  51. 

The  m.m.f.  required  to  send  the  no-load  flux  through  the 
magnetic  circuit  is  9990  ampere-turns,  of  which  8280  ampere- 
turns  are  required  for  the  gap  and  tooth.  The  voltage  generated 
due  to  this  flux  is  240. 


60 


ELECTRICAL  MACHINE  DESIGN 


At  full  load  the  m.m.f.  at  one  pole  tip 

=  8280+4700  =  12980  ampere-turns, 
and  that  at  the  other  pole  tip 

=  8280  -  4700  =  3  580    ampere-turns. 

The  flux  crossing  the  air  gap  is  reduced  in  the  ratio 

Fig.  53,  and,  due  to  this  reduction  in  flux,  the  voltage  generated 
is  reduced  from  240  to  235.5. 


2a4  6  8  10  12      d     14.xl03 

Ampere  Turns  per  Pole 

FIG.  53. — No-load  and  full-load  saturation  curves. 


To  maintain  the  generated  voltage  at  this  reduced  value  of 
235.5  volts  it  is  necessary  to  increase  the  no-load  field  excitation 
of  9990  ampere-turns  by  1340,  the  demagnetizing  ampere-turns 
per  pole. 

The  terminal  voltage  is  less  than  the  generated  voltage  of 
235.5  by  8.7,  the  voltage  required  to  send  the  full-load  current 
through  the  armature,  brushes  and  series  field.  The  full  load 
saturation  curve  is  drawn  parallel  to  the  no-load  saturation  curve 
through  the  point  g  so  found. 


ARMATURE  REACTION  61 

In  order  to  get  the  same  flux  across  the  air  gap  at  full-load  as 
at  no-load  the  field  excitation  has  to  be  increased  over  its  no-load 
value  so  as  to  counteract  the  effect  of  the  m.m.f.  of  the  armature. 
Due  to  this  increase  in  excitation  the  leakage  flux  is  increased, 
so  that  the  leakage  factor  is  greater  at  full-load  than  at  no-load, 
and  still  more  excitation  is  required  on  account  of  the  resulting 
increase  in  the  pole  and  yoke  densities.  This  latter  increase  in 
excitation,  however,  cannot  readily  be  calculated. 

52.  Relative  Strength  of  Field  and  Armature  M.M.FS.—  Inspec- 
tion of  Fig.  49  will  show  that  if  the  armature  current  be  increased 

to  such  a  value  that  the  cross-magnetizing  ampere-turns  of  the 

2? 
armature  at  the  pole  tips,  namely  \  <[>-Ic  ampere-turns,  becomes 

equal  to  the  ampere-turns  for  the  tooth  and  gap  due  to  the  main 
field  excitation,  then  the  flux  density  will  be  zero  under  the  pole 
tip  toward  which  the  brushes  have  been  shifted  in  order  to  help 
commutation,  so  that  to  obtain  a  reversing  field  it  is  necessary  that 

the  ampere-turns  of  the  main  field  for  gap  and  tooth  be  greater 
17 

than  J  </>-Ic. 

To  get  a  reasonably  strong  field  for  commutating  purposes, 
experience  shows  that  the  above  value  at  full  load  should  not  be 
less  than  1.7,  and  the  higher  the  value  the  better  the  commuta- 
tion, other  things  being  equal,  but  at  the  same  time  the  more 
expensive  the  machine  due  to  the  extra  field  copper  required. 

y 

The  quantity  \  <1>—IC  is  equal  to  $  (armature  ampere-turns  per 

ampere-turns  of  main  field  for  gap  and  tooth 
armature  ampere-turns  per  pole  at  full  load 


=  1.2  ............................................  (6) 

a  formula  which  is  greatly  used  in  dynamo  design.  In  deriving 
this  formula  it  is  assumed  that  the  m.m.f  of  the  series  field  is 
just  able  to  counteract  the  demagnetizing  effect  of  the  armature 
m.m.f.  In  the  case  of  a  shunt  motor,  where  there  is  no  series 
winding,  and  where  the  shunt  excitation  is  constant,  the  ampere- 
turns  of  the  main  field  for  the  gap  and  tooth  =1.2  (armature 
ampere-turns  per  pole)  +  the  demagnetizing  ampere-turns. 


CHAPTER  VII 


DESIGN  OF  THE  MAGNETIC  CIRCUIT 

The  problem  to  be  solved  in  this  chapter  is,  given  the  armature 
of  a  machine  and  also  its  rating  to  design  the  poles,  yoke,  and 
field  coils. 

53.  Field  Coil  Heating.1 — Fig.  54  shows  one  of  the  poles  of  a 
D.  C.  machine  with  its  field  coil.  The  exciting  current  //  passes 
through  this  coil  and  gradually  raises  its  temperature  until  the 
point  is  reached  where  the  rate  at  which  heat  is  dissipated  by  the 
coil  is  equal  to  the  rate  at  which  it  is  generated  in  the  coil. 


<-df 


FIG.  54.— D.-C.  field  coil. 


The  hottest  part  of  the  coil  is  at  A,  and  the  heat  has  to  be 
carried  from  this  point  to  the  radiating  surfaces  B,  C,  D  and  E, 
so  that  there  must  be  a  temperature  gradient  between  A  and  the 
radiating  surface  of  the  coil;  Fig.  55  shows  the  temperature 
at  different  points  in  the  thickness  of  a  field  coil. 

The  maximum  temperature  of  the  coil  limits  the  amount  of 
current  that  it  can  carry  without  injury,  but  this  temperature  is 
difficult  to  measure.  The  external  temperature  of  the  coil  can 
be  taken  by  means  of  a  thermometer,  and  the  mean  tempera- 

*A  good  summary,  with  complete  references,  of  the  work  published 
on  field  coil  heating  will  be  found  in  a  paper  by  Lister:  Journal  of  the 
Institution  of  Electrical  Engineers,  Dec.,  1906. 

62 


DESIGN  OF  MAGNETIC  CIRCUIT 


63 


ture  can  be  found  by  the  increase  in  resistance  of  the  coil,  since 
the  resistance  of  copper  at  any  temperature  t  =  Rt  =  R0(l  + 
0.004  t)  where  R0  is  the  resistance  at  0°  C.  and  t  is  in  centigrade 
degrees. 

It  is  found  that  the  ratio  between  the  maximum  and  the  mean 
temperature  seldom  exceeds  1.2,  while  that  between  the  mean 
and  the  external  surface  temperature  varies  from  about  1.4  to  3. 
The  latter  figure  is  found  in  some  of  the  early  machines  whose 
field  coils  were  covered  with  tape  and  rope.  When  the  coil  is 
insulated  as  shown  in  Fig.  36  the  ratio  of  the  mean  temperature 
to  that  of  the  external  surface  will  be  approximately  1.5  if  the 


100 

X 

^^ 

^ 

-~^ 

""X 

Degrees  Cent.  Rise 

8  fe  §  § 

/ 

X 

s. 

/ 

\ 

\ 

s05 

Q 

\ 

0 

a 

I 

rn 

I 

FIG.  55. — Temperature  gradient  in  field  coils. 

external  surface  is  left  bare  except  for  the  d.c.c.  on  the  wire,  the 
whole  coil  impregnated  with  compound,  and  the  coil  about 
2  in.  thick;  the  compound  is  a  better  conductor  of  heat  than  the 
air  which  it  replaces  and  is  also  a  better  insulator.  If  two  layers 
of  half-lapped  tape  be  put  on  the  external  surface  of  the  coil 
the  ratio  will  increase  to  about  1.7  and  if  in  addition  a  layer  of 
cardboard  1/16  in.  thick  be  put  on  the  external  surface,  as  was 
formerly  done  to  protect  the  coil,  the  ratio  will  exceed  2.  These 
are  average  figures  and  may  vary  considerably  since  they  are 
affected  by  the  fanning  action  of  the  armature,  the  kind  of 
compound  used,  the  thickness  of  the  insulation  on  the  wire,  the 
radiating  power  of  the  poles  and  yoke  on  which  depends  the 
radiating  power  of  the  surface  D. 

The  heating  constants  for  field  coils  are  figured  in  many  differ- 
ent ways,  depending  on  what  is  taken  for  the  radiating  surface. 
While  it  is  true  that  all  the  surfaces^  B,  C,  D  and  E,  are  active  in 
radiating  heat,  yet  they  are  not  all  equally  effective,  and  for  that 


64 


ELECTRICAL  MACHINE  DESIGN 


reason,  and  also  for  convenience,  the  radiating  surface  is  taken  as 
the  external  surface  B. 

For  impregnated  coils  without  any  insulating  material  on  the 
external  surface  other  than  that  on  the  wire  itself,  the  watts 
that  can  be  radiated  per  square  inch  of  the  external  surface 
for  a  temperature  rise  of  40°  C.  on  that  surface,  which  corre- 
sponds to  an  average  temperature  rise  of  60°  C.  and  a  maximum 
temperature  rise  of  70°  C.,  varies  from  0.5  to  1.0  depending  on  the 
length  of  the  coil  and  also  on  the  peripheral  velocity  of  the  arma- 
ture. The  effect  of  the  fanning  action  of  the  armature  can 
readily  be  understood  so  that  the  slope  of  the  curves  in  Fig.  56 
needs  no  explanation.  It  will  be  seen  from  this  diagram  that  a 
short  coil  is  more  effective  than  a  long  one  because  the  ratio  of  the 
total  radiating  surface  B,  C,  D  and  E}  to  the  external  surface  B  on 
which  the  constants  are  based,  is  greater  in  the  short  than  in 
the  long  coil,  and  also  because  only  that  portion  of  the  long  coil 
which  is  near  the  armature  is  affected  by  the  armature  fanning. 


1.2 


0.8 


- 

wo  0.4 


$ 


1  2  3  4  5  6xlO~3 

Peripheral  Velocity  of  the  Armature 
in  Ft.  per  Min. 

FIG.  56. — Field  coil  heating  constant. 

The  radiating  surface  of  a  coil  is  often  increased  by  putting 
in  ventilating  openings  as  shown  in  Fig.  37;  this  method  would 
seem  to  double  the  radiating  surface,  but  the  sides  of  the  venti- 
lating opening  are  not  so  effective  as  either  the  inner  or  the 
outer  surface  of  the  coil.  For  this  type  of  field  coil,  where  the 
individual  coils  are  1  in.  thick  and  spaced  i  in.  apart,  the  watts 
per  square  inch  of  external  surface  can  be  increased  50  per  cent, 
over  the  values  given  in  Fig.  56. 


DESIGN  OF  MAGNETIC  CIRCUIT 

54.  The  Size  of  Wire  for  Field  Coils : 

If  Ef  is  the  voltage  across  each  field  coil, 
//  is  the  current  in  the  coil, 
Tf  is  the  number  of  turns  in  the  coil, 
MT  is  the  length  of  the  mean  turn  of  the  coil  in  inches, 
M  is  the  section  of  the  wire  used  in  circular  mils. 


65 


then  the  resistance  of  the  coil 


EMTxT- 


since  the  resistance 


of  copper   is   approximately  1   ohm    per  circular    mil   per  inch 
length, 


and 


(7) 


so  that  for  a  given  machine  the  size  of  field  wire  is  fixed  as  soon 
as  the  ampere-turns  and  the  voltage  per  coil  are  known. 


U.i 

1 

<H 

o? 
«  0.6 

1 
0.5 

\ 

4  x£> 

o- 

1 

\ 

«-> 

-ay? 

*^L 

-D- 

\ 

S  -t 

\ 

•> 

N 

S  T 

^ 

^^» 

\ 

\ 

\, 

\ 

' 

\ 

2            6      8    10    12    14    16    18    20   22    Z 
B.  &  S.  Gage 

FIG.  57. — Space  factor  for  wire. 


55.  The  Length  Lf  of  the  Field  Coil.— The  watts  radiated  from 
the  coil  shown  in  Fig.  54  =  external  surf  ace  X  watts  per  square 
inch.  The  total  section  of  copper  in  the  coil  =  dj  xLf  Xsf  square 
inch,  where  s/.,  the  space  factor  of  the  wire,  is  the  section  of  the 
wire  divided  by  the  space  that  the  wire  takes  up  in  the  coil  and 
is  got  from  Fig.  57. 

The  section  of  the  wire  in  the  coil  =   ^—L—    square  inches 

dfXLjXs/X  1,270,000    . 

— ^ —  -  circular  mils. 

1f 
-AT 


66  ELECTRICAL  MACHINE  DESIGN 

M  TX  T-r 

The  watts  loss  per  coil  =  —  -    —  lXlf2  and,  substituting  for  M, 


dfXLfXsfX  1,270,000 
The  watts  loss  per  coil  also  =  external  surface  of  coil  X  watts  per 

square  inch. 
=  external    periphery    of    coilx£/X 

watts  per  square  inch. 

Therefore,  equating  these  two  values  together, 

mean  tumX(IfTf)2 


L'/- 


ext.  periphery X watts  per  sq.  in.  XdfXsfX  1,270,000 


j  T   _  IfTf    I  mean  turn  ,~. 

1  =  1000  \  ext.  periphery  X  watts  per  sq.  in.  Xd/Xs/X  1.27 
In  order  to  have  an  idea  as  to  the  value  of  I/  found  from  the 
above  equation  assume  the  following  average  values: 
sfj  the  space  factor  =0.6 
df,  the  coil  depth      =2.0  in. 
watts  per  square  inch    =0.6. 
external  periphery         =  1 . 2  X  mean  turn. 

T  T7 

then  Lf,  the  radial  length  of  coil  space,  =~n  approxi- 


mately. 

56.  Weight  and  Depth  of  Field  Coils.— The  weight  of  the  field 
coil  =  0.32 XMTxLfXdfXsf.  pounds,  where  0.32  is  the  weight 
of  a  cubic  inch  of  copper, 

_  IfTf    I  mean  turn 

'     1000  \ ext.  periphery  X  watts  per  sq.  in. XdfXsfXl.27 

a  constant 
=IfTf  -   —= —  approximately,  for  a  given  machine, 

therefore  the  weight  of  the  field  coil 


/ 

=  a  constant  Vo/  for  a  given  machine. 

This  may  be  interpreted  as  follows:  the  larger  the  value  of 
df,  the  shorter  the  length  L/,  the  smaller  the  radiating  surface, 
and  therefore  the  lower  the  value  of  permissible  loss  per  coil, 
Since  the  section  of  the  field  coil  wire  is  fixed,  because,  as 
shown  in  Art.  54,  it  depends  only  on  the.  ampere-turns  and 
the  voltage  per  coil,  a  lower  permissible  loss  can  only  be  ob- 


DESIGN  OF  MAGNETIC  CIRCUIT  67 

tained  by  a  smaller  value  of  //  and  therefore  by  a  larger  value  of 
Tf  and  a  more  expensive  coil.  It  would  seem  then  that  the 
thinner  the  field  coil  the  cheaper  the  machine,  but  it  must  not 
be  overlooked  that,  as  the  value  of  df  becomes  less,  and  therefore 
the  cost  of  the  field  copper  decreases,  the  value  of  Z//  increases 
and  therefore  the  cost  of  the  poles  and  yoke  also  increases.  The 
value  of  df  for  minimum  cost  of  field  system  must  take  this  into 
account  and  can  readily  be  determined  by  trial;  an  average  value 
for  df  is  2  in. 

57.  Procedure  in  the  Design  of  the  Field  System  for  a  Given 
Armature. 

(1)  Find  the  air  gap  clearance  as  follows: 

AT  'g+tj  the  ampere-turns  per  pole  for  gap  and  teeth, 

=  1.2   (armature  AT  per  pole)  for  generators, 

=  1.2  (armature  AT  per  pole)  +  demagnetizing  AT  per 

pole,  for  shunt  motors;   see  page   61. 

From  the  armature  data,  ATt,  the  ampere-turns  per  pole  for  the 

teeth,    can    be    found: 

B  XCX<? 

AT  g,  the  gap  ampere-turns,  =    g  Q  ^  —  from  formula'  3,  page 

o  -  Z 

48,  from  which  d  can  be  found. 

(2)  Draw  the  saturation  curves. 

Before  this  can  be  done  it  is  necessary  to  determine  approxi- 
mately the  dimensions  of  the  magnetic  circuit,  which  is  done  as 
follows: 

It  is  assumed  that  the  no-load  excitation  =  1.25(ATg+t)f  and 

L   ...       no-load  amp.-turns 
that  L/ss—  -  approximately,  see  Art.  55,  page 

lUUU 

66;  this  coil  length  is  increased  30  per  cent,  to  allow  for  the  series 
field  should  such  be  required. 

The  section  of  the  pole  is  got  by  assuming  that  the  pole  density 
is  95,000  lines  per  square  inch  and  that  the  leakage  factor  has  the 
value  given  in  the  table  on  page  53;  then  Ap,  the  pole  area  in 

< 

square  inches,  =5 


The  yoke  area  is  found  in  a  similar  way  by  assuming  that  the 
yoke  density  is  75,000  lines  per  square  inch  for  cast  steel  and 
40,000  lines  per  square  inch  for  cast  iron. 

The  magnetic  circuit  may  now  be  drawn  in  to  scale  and  the 
saturation  curves  determined;  these  may  require  a  slight  modi- 
fication as  the  work  proceeds. 


68 


ELECTRICAL  MACHINE  DESIGN 


(3)   Design  the  shunt  field  coil. 

Find  the  no-load  excitation  from  the  saturation  curve. 

Find  M  the  size  of  field  coil  wire  from  the  formula 


IfTfXMT 


;  see  Art.  54,  page  65. 


,  the  volts  per  coil,= 


terminal  voltage 
poles 


Xk 


where  k  =  0.8  for  compound  generators;  which  leaves  20  per  cent, 
of  the  terminal  voltage  to  be  absorbed  by  the  field- 
circuit  rheostat,  so  that  the  shunt  excitation  may  be 
increased  20  per  cent,  over  its  normal  value  should 
that  be  desired  at  any  time. 

k  =  1.0  for  shunt  motors. 

k  for  shunt   generators   is  determined  for  each  separate 
case;  there  should  be  enough  field  regulation  to  allow 
normal  voltage  to  be  maintained  from  no-load  to  the 
desired  overload. 
Lf  is  found  from   the  formula 


T     -Ml     - 
'"lOOOXext. 


mean  turn 


periphery Xwattspersq.  in.  XdfXsfX  1.27  ' 
see  Art.  55,  page  66. 

Tf  is  the  number  of  turns  of  wire  of  section  M  that  will  fill  up 
the  space  LfXdf. 

(4)   Design  the  Series  field  coil. 


FIG.  58. — Series  field  coil. 

The  series  excitation  at  full-load  is  found  from  the  saturation 
curves  and  is  the  difference  between  the  excitation  for  the 
required  terminal  voltage  found  from  the  full-load  saturation 
curve  and  the  shunt  excitation  at  the  same  voltage. 

series  excitation     .  . 
.    The  number  of   series  turns  =  fu0.load  current;  this  value  is 


DESIGN  OF  MAGNETIC  CIRCUIT  69 

generally  increased  20  per  cent,  on  new  designs  because  of  the 
difficulty  in  predetermining  exactly  the  full-load  saturation 
curve;  when  the  coil  is  shaped  as  shown  in  Fig.  58  there  must 
always  be  a  half  turn  in  the  coil;  the  coil  shown  has  2J  turns. 
The  current  density  in  the  series  coil  and  also  the  value  of 
watts  per  square  inch  external  surface  are  20  per  cent,  greater 
than  in  the  shunt  coils  of  the  same  machine,  because  the  series 
coils  are  closer  to  the  armature  and,  therefore,  better  cooled  by  its 
fanning  effect. 

Example.  —  The  armature  of  a  10-pole,  400-kw.,  240-volt  no-load,  240- 
volt  full-load,  1670  amp.,  200  r.p.m.  generator  is  shown  to  scale  in  Fig.  41  ; 
it  is  required  to  design  the  field  system,  which  is  not  supposed  to  be  given. 

(1)  Find  the  air-gap  clearance. 

,       800X167 

Armature  ampere-turns  per  pole  =  =6700 

&  X  1U 

Ampere-  turns  per  pole  (gap  +  tooth)  =1.2X6700  =  8100 
Ampere-  turns  per  pole  for  the  tooth  are  found  as  'follows: 

=  240X60><108 
a~     800X200~~ 

=  9X106 

200 
minimum  tooth  area  per  pole  =  0  .  43  X  -^-  X  0  .  7  X  9  .  45 

=  57  sq.  in. 

9X  108 

maximum  tooth  density  =  —  -==— 

o  • 

=  158,000  lines  per  square  anch,  apparent. 
=  150,000  lines  per  square  inch,  actual, 

from  Fig.  43. 
tooth  taper  =  A;  =  1.1  2 
ampere-turns  per  pole  for  the  teeth  =  1300X  1.6,  from  Fig.  44. 

=  2080 

Ampere-turns    per   pole  for  the  gap  =  8100  —  2080 

=  6020 

,       ..  9X106 

Apparent  gap   density  =  18  2XO  7xl2 

=  59,000  lines  per  square  inch. 
_  3.2X6020 
~~6pOO~~ 
=  0.328 
therefore  C  =1.12  from  Fig.  40,  page  44, 

and        d  =0.29  (make  gap  clearance  =0.3  in.) 

(2)  Draw  the  saturation  curves. 
No-load  excitation  =1.25X8100 

=  10,100  amp.-turns  approximately. 
10,100 
'  =  =      m>  aPProximately- 


Allow  30  per  cent,  more  for  the  series  coil,  so  that  the  coil  space  =  13  in. 


70  ELECTRICAL  MACHINE  DESIGN 


™  9X106X1.18 

The  pole  area  =  -^^- 

I 

The  yoke  area  = 


95,000 

=  112  sq.  in.  approximately. 
9X103X1.18 


2X40,000 
=  132  sq.  in.  approximately. 

From  the  dimensions  found  above  the  magnetic  circuit  is  drawn  to  scale 
and  the  no-load  and  full-load  saturation  curves  are  determined.  For  the 
machine  in  question  the  curves  are  shown  in  Fig.  53. 

(3)  Design  the  shunt  coil. 

The  no-load  excitation   =9990  amp.-turns 

Ef,  the  volts  per  coil       =240^0-8  =19 

MT,  the  mean  turn  =53  in. 

External  periphery  of  the  coil  =61  in. 

QQQfl  V  ^ 

Size  of  shunt  coil  wire   =       "*=  28,000  circular  mils; 

iy 

use  No.  5|  B  &  S.  gauge,  a  special  size  between  No.  5  and  No.  6,  which 
has  a  section  of  29,500  circular  mils  and  a  diameter  when  insulated  with 
d.c.c.  of  0.19  in.  Where  such  odd  sizes  are  not  available  the  coil  can  be 
made  up  of  the  proper  number  of  turns  of  No.  5  wire  in  series  with  the 
proper  number  of  turns  of  No.  6,  so  as  to  have  the  same  resistance  as  that  of 
a  coil  made  with  wire  of  a  section  of  28,000  circular  mils. 
L/  =  10.5  in.  assuming  that  d/  =  2  in. 

s/=0.65 
watts  per  sq.  in.  =0.6 

o 

The  number  of  layers  of  wire  in  a  depth  of  2  in.  =^---Q  =  10. 
*  \)  .  j.y 

The  number  of  turns  per  layer  in  a  length  of  10.5  in.  =  —^-=55. 

u.iy 

The  number  of  turns  per  coil  =10X55  =  550. 

9990 

The  shunt  current  =    =18.2  amp. 
ooO 

29  500 

The  current  density  in  the  field  coil  wire  =  ^-5-0"  =  1600  cir-  m^s  Per  amp. 

lo>2 

(4)  Design  the  series  coil. 

The  excitation  at  full-load  and  normal  voltage  =12,800  amp.-turns. 
The  shunt  excitation  at  normal  voltage  =  9,990  amp.-turns. 

Therefore  the  series  ampere-turns  at  full  load     =  2810 
The  series  turns     =2.5 


The  series  current  =^~~  =  1  120 
2.5 

The  current  in  the  series  shunt  =1670  —  1120  =  550  amperes 

i  Ano 

The  current  density  in  the  series  coil  =^r-s-  =  1330  circular  mils  per  amp. 

1  .2 

The  size  of  the  series  coil  wire  =  1  330  X  1120 

=  1,500,000  circular  mils 
=  1.2  sq.  in. 


DESIGN  OF  MAGNETIC  CIRCUIT  71 

The  resistance  of  2.5  turns  of  this  wire 


The  voltage  drop  in  one  series  coil  =  8.8X  10~5X  1120 

=  0.1  volts 
The  loss  in  one  series  coil  =0.1  X  1120 

=  112  watts 
The  permissible  watts  per  square  inch  external  surface  =0.6X  1.2  =  0.72. 

112 

The  necessary  radiating  surf  ace  =  TT^S  =155  sq.  in. 

U.  I  £i 

The  external  periphery  of  the  coil  =61  in.  approximately 
The  length  L/  of  the  series  coil=  -^-  =2.5  in. 

_  .  ,      .,     .         section  of  wire 
The  thickness  of  the  series  field  coil  wire  =  —     —  ^  — 

Lf 
1.2 
2.5 

=  0.5  in. 

The  section  of  the  wire  is  made  up  of  four  strips  in  parallel  each  0.125X2.5 
section  so  that  the  coil  may  be  readily  bent  to  shape. 


CHAPTER  VIII 
COMMUTATION 

The  direction  of  the  current  in  the  conductors  of  a  D.-C. 
machine  at  any  instant  is  shown  in  Fig.  59;  therefore,  as  the 
armature  revolves  and  conductors  pass  from  one  side  of  the 
neutral  line  to  the  other,  the  current  in  these  conductors  must  be 
reversed  from  a  value  Ic  to  a  value  —  7C,  where  7C  is  the  current 
in  each  conductor. 


FIG.  59. — Direction  of  current  in  a  D.-C.  armature. 

Figure  61  shows  part  of  a  full-pitch  double-layer  multiple 
winding  with  two  conductors  per  slot  and  with  the  coils  M 
undergoing  commutation,  and  Fig.  60  shows  part  of  the  corre- 
sponding ring  winding.  It  may  be  seen  from  diagrams  A  and 
E  that  the  current  in  coils  M  is  reversed  as  the  armature  moves 
so  that  the  brushes  change  from  commutator  segments  1  and  5 
to  segments  2  and  6. 

58.  Resistance  Commutation. — Let  the  coils  M  be  in  such  a 
position  between  the  poles  TV  and  S  that,  during  commutation, 
they  are  not  cutting  any  lines  of  force  due  to  the  m.m.f.  of  the 
field  and  armature,  and  let  the  contact  resistances  rl  and  r2, 
diagram  B,  between  the  brush  and  segments  5  and  6,  be  so  large 

72 


COMMUTATION 

N  S 


73 


FIG.  60.  FIG.  61. 

Stages  in  the  process  of  commutation. 


74  ELECTRICAL  MACHINE  DESIGN 

that  the  effect  of  the  resistance  and  self  induction  of  the  coils 
M  may  be  neglected. 

In  the  position  shown  in  diagram  B  the  contact  area  between 
the  brush  and  segment  5  is  large  while  that  between  the  brush 
and  segment  6  is  small,  and  the  current  2IC}  which  passes  through 
the  brush,  divides  up  into  two  parts  which  are  proportional  to 
the  areas  of  contact  between  the  brush  and  segments  5  and  6 
respectively,  and  are  equal  to  Ie+i  and  Ic  —  i. 

In  the  position  shown  in  diagram  C  the  two  contact  areas  are 
equal  and  there  is  no  tendency  for  current  to  flow  round  the 
coil  M. 

In  the  position  shown  in  diagram  D  the  contact  area  between 
the  brush  and  segment  5  is  small  while  that  between  the  brush 
and  segment  6  is  large,  and  the  current  21 c  which  passes  through 
the  brush  divides  up  into  two  parts  as  shown  in  the  diagram; 
the  current  i  in  coil  M  now  passes  in  a  direction  opposite  to 
that  which  it  had  in  diagram  A.  As  the  contact  area  with  seg- 
ment 5  decreases,  the  value  of  the  current  i  which  passes 
round  coil  M  increases  until,  at  the  instant  shown  in  diagram  E, 
this  current  is  equal  to  —Ic. 

By  this  action  of  the  brush  the  current  in  the  coil  M  is  reversed 
or  commutated  while  the  armature  moves  through  the  distance 
of  the  brush  width,  and  the  variation  of  current  with  time  is 
plotted  in  curve  1,  Fig.  62,  and  follows  a  straight  line  law. 

59.  Effect  of  the  Self-induction  of  the  Coil. — The  resistance 
of  the  coil  undergoing  commutation  is  generally  so  low  that  its 
effect  can  be  neglected,  but  the  effect  of  self-induction  must  be 
considered. 

The  current  i  in  the  coils  M  sets  up  lines  of  force  which  link 
these  coils.  As  this  current  reverses  the  lines  of  force  also 
reverse,  as  shown  in  diagrams  B  and  D,  and  the  change  of  flux 
generates  an  e.m.f.  in  each  coil  M  which  is  generally  called  its 
e.m.f.  of  self-induction.  It  is  important  to  notice  however  that 
part  of  the  flux  which  links  one  of  the  coils,  say  M,  is  due  to 
current  in  the  coil  Afx  on  one  side  and  to  current  in  the  coil  M2 
on  the  other  side,  so  that  this  generated  e.m.f.  is  really  an  e.m.f. 
of  self  and  mutual  induction. 

The  e.m.f.  of  self  and  mutual  induction  opposes  the  change  of 
current  which  produces  it,  so  that  at  the  end  of  half  of  the 
period  of  commutation  the  current  in  the  coils  M  has  not  be- 
come zero  but  has  still  the  value  cd,  curves  2,  3  and  4,  Fig.  62; 


COMMUTATION  75 

these  curves  show  the  variation  of  current  with  time  for  differ- 


ent  values  of  the  ratio  -=  —  £=  where: 
L  +  M 

R  is  the  resistance  of  the  total  brush  contact  in  ohms, 

Tc  is  the  time  of  commutation  in  seconds, 

L   is  the  coefficient  of  self-induction  of  one  coil  M  in  henries, 

M  is  the  coefficient  of  mutual  induction  between  coil  M  and 

coils  M!  and  M2  in  henries. 

The  equation  from  which  these  curves  were  plotted  is  derived 
as  follows: 

The  difference  of  potential  between  a  and  b,  diagram  B,  Fig.  61, 
—  (Ic+i)?!  —  (Ic  —  i)r2  and  this  must  be  equal  and  opposite  to  the 

generated  voltage  —  (L  +  M)  -=- 

or  (In+i)ri-(Ic-i)r2 

If  now  R  and  Tc  have  the  values  already  mentioned,  and  t  is 
the  time  measured  from  the  start  of  commutation 


therefore  (Ie+i)R  (7^7)  +(L  +  M)  ~-(Ic-i)R  (^)  =0 

\J-  C        "'  (*" 

,  di         I  RTC  \    (Ic+i     Ic-i 

and  -jT=  —  (  T  .  *,)    1™ ~t r~ 

at          \L  +  M]    \lc  —  t         t 

The  results  from  this  equation  are  plotted  in   Fig.   62   for 

7?/77 

different  values  of  the  ratio  /r      °    ' 

(L+M) 

60.  Current  Density  in  the  Brush. — By  the  use  of  the  values  of 
i  plotted  in  Fig.  62  the  value  of  the  current  Ic+i  flowing  from 
the  brush  to  segment  5  can  be  determined,  and  from  it  the  cur- 
rent density  in  the  brush  tip  s  at  any  instant  can  be  obtained. 
This  quantity  is  plotted  against  time  in  Fig.  63,  and  it  will  be 

7P71 
seen  that,  for  values  of  T  .Z*  less  than  1,  the  current  density  in 

the  brush  tip  s  becomes  infinite,  and  due  to  the  concentration  of 
energy  at  this  tip  sparking  takes  place. 

The  criterion  for  sparkless  commutation  then  is  that 


L+M 

1  For  the  solution  of  this  equation  see  Reid  on  Direct  Current  Commuta- 
tion.    Trans,  of  A.  I.  E.  E.,  Vol.  24,  1905. 


76 


ELECTRICAL  MACHINE  DESIGN 


be  greater  than  1,  and  perfect  commutation  is  denned  as  such  a 
change  of  current  in  the  coil  being  commutated  that  the  current 
density  over  the  contact  surface  between  the  brush  and  the 
commutator  segment  is  constant  and  uniform. 


i 


X 


\\ 


\v 


0    0.1  0.2  0.3  0.4  0.5  0.6   0.7  0.8   0.9 


Time  from  Start  of  Commutation 
FIG.  62. 


0.1  0.2   0.3  0.4  0.5  0.6  0.7  0.8  0.9    Tc 
Time  from  Start  of  Commutation 

FIG.  63. 


RT, 


Curve  l,-r+M- 

Curve  2. —  •=- — j^  = 
RTC 


Curve  3. — 


L  +  M 


Curve  4.— =5^5= 


infinity. 

1.0 

0.5 
Current  in  the  short-circuited  coil  and  current  density  at  the  brush  tip. 

61.  The  Reactance  Voltage. — The  above  criterion  for  sparkless 
commutation  is  used  in  practice  in  a  slightly  different  form  for, 

7PT7 
if  ,.      c    must  be  greater  than  1 

then  R  must  be  greater  than  — ^ — 


and  21  CR  greater  than 


21 


This  latter  quantity  is  called  the  average  reactance  voltage, 
and  is  the  e.m.f.  of  self  and  mutual  induction  of  the  coil  being 
commutated  on  the  assumption  that  the  current  varies  from  Ic 
to  —  7C  according  to  a  straight  line  law.  This  average  reactance 
voltage  then  should  always  be  less  than  2ICR  the  voltage  drop 
across  one  brush  contact. 

62.  Brush  Contact  Resistance.  —  Curve  1,  Fig.  64,  shows  the 


COMMUTATION 


77 


value  of  the  resistance  of  unit  section  of  brush  contact  plotted 
against  current  density  in  that  contact;  the  resistance  decreases 
as  the  current  density  increases  and  for  higher  values  than  35 
amperes  per  square  inch  it  varies  almost  inversely  as  the  current 
density  and  the  voltage  drop  across  the  contact  becomes  prac 
tically  constant,  as  shown  in  curve  2,  Fig.  64. 

Such  curves  of  brush  resistance  are  obtained  by  testing  the 
brushes  on  a  revolving  collector  ring  and  allowing  sufficient 
time  to  elapse  between  readings  to  let  the  conditions  become 
stationary. 


i.o 


0.8 


0.6 


0.4 


>  0.2 


\ 


.06 


.04 


.02 


10   20  30   40  50  60  70  80  90  100 
Amperes  per  Sq.  Inch 

FIG.  64. — Brush-contact  resistance  curves. 

The  resistance  from  ring  to  brush  is  generally  greater  than 
that  from  brush  to  ring  by  an  amount  which  varies  with  the 
material  of  the  brush. 

It  would  seem  that,  by  neglecting  the  effect  of  the  variation  of 
contact  resistance  with  current  density,  as  was  done  in  Art.  59, 
the  results  there  obtained  would  be  rendered  of  little  practical  im- 
portance, it  is  found,  however,  that  the  variation  in  resistance  is 
largely  a  temperature  effect  and  that  at  constant  temperature 
the  contact  resistance  does  not  vary  through  such  extreme 
limits,  also  that,  due  to  the  thermal  conductivity  of  carbon,  the 
temperature  difference  between  two  points  on  a  brush  contact  is 
not  very  great. 

Suppose  that,  having  reached  the  value  of  10  amperes  per 
square  inch,  and  the  resistance  having  become  stationary  at 
0.06  ohms  per  square  inch,  see  Fig.  64,  the  current  density  were 


78 


ELECTRICAL  MACHINE  DESIGN 


suddenly  increased  to  40  amperes  per  square  inch;  the  re- 
sistance in  ohms  per  square  inch  would  not  fall  suddenly  to 
0.023  but  would  have  a  value  of  about  0.06  and  this  would 
gradually  decrease  until,  after  about  20  minutes,  the  resistance 
would  have  reached  the  value  of  0.023,  the  value  which  it  ought 
to  have  according  to  curve  1,  Fig.  64.  This  explains  why  a 
machine  will  stand  a  considerable  overload  for  a  short  time 
without  sparking,  whereas  if  the  overload  be  maintained  the 
machine  will  begin  to  spark  as  the  brush  temperature  increases 
and  the  contact  resistance  decreases. 

Sparking  is  cumulative  in  its  effect  because  slight  sparking 
raises  the  temperature  of  the  brush  contact,  which  reduces  the 
contact  resistance  and  causes  the  operation  to  become  worse. 

63.  Brush  Pressure. — The  brush  contact  resistance  is  found  to 
decrease  as  the  brush  pressure  increases  and  as  the  rubbing 
velocity  decreases,  but  these  effects  can  be  neglected  in  any 
study  of  commutation  since  the  change  due  to  rubbing  velocity 
is  small,  while  the  biush  pressure  is  fixed  by  the  service  and  is 
made  as  small  as  possible.     The  brush  pressure  is  seldom  less 
than  1.5  Ib.  per  square  inch  of  contact  surface  because  at  lower 
pressures  the  brushes  are  liable  to  chatter,  while  if  the  pressure  be 
too  great  the  brushes  cut  the  commutator  if  they  are  hard  or  wear 
down  and  smear  the  commutator  if  they  are  soft.     A  brush  pres- 
sure greater  than  2  Ib.  per  square  inch  is  seldom  exceeded  except 
for  street  car  motors,  in  which  case  the  vibration  of  the  machine 
itself  is  excessive,  and  pressures  as  high  as  5  Ib.  per  square  inch 
have  to  be  used  to  prevent  undue  chattering  of  the  brushes. 

64.  Energy  at  the  Brush  Contact. — The  criterion  for  sparkless 
commutation  is  that  the  energy  at  the  brush  tip,  which  is  pro- 
portional to  the  current  density  in  that  tip,  shall  not  become 
infinite.     The  average  energy  expended  at  the  brush  contact 
must  also  be  limited  as  may  be  seen  from  the  following  table: 


Kind  of  brush1 

Current  density 

Volts  across 
one  contact 

Very  soft  carbon 

50  —  70  amp   per  so   in 

0  6-0  4 

Soft  carbon   

40—65  amp.  per  sq.  in  

0  7-0  55 

Fairly  hard  carbon  
Very  hard  carbon  

30-45  amp.  per  sq.  in  
25-40  amp.  per  sq.  in  

1.1-0.9 
1.5-1.2 

Arnold,  Die  Gleichstrom-machine,  Vol.  1,  page  351. 


COMMUTATION 


79 


The  product  of  amperes  per  square  inch  and  volts  drop  across 
one  contact  has  an  average  value  of  35  watts  per  square  inch. 
It  must  be  understood  that  these  figures  are  for  machines  which 
operate  without  sparking  and  without  shifting  of  the  brushes 
from  no  load  to  25  per  cent,  overload,  but  have  not  necessarily 
what  was  defined  in  Art.  60,  page  76,  as  perfect  commutation. 
The  better  the  commutation  the  more  nearly  uniform  the  current 
density  in  the  brush  contact  and  the  higher  the  average  current 
density  that  can  be  used  without  trouble  developing. 

65.  Calculation  of  the  Reactance  Voltage  for  Machines  with 
Full-pitch  Multiple  Windings. — Consider  first  the  case  where 
there  are  T  turns  per  coil  and  the  brush  covers  only  one  segment, 
as  shown  in  Fig.  65.  The  winding  is  of  the  double  layer  type  and 
has  two  coil  sides  per  slot;  a  section  through  one  slot  is  shown 
at  S,  Fig.  65,  for  the  case  where  7"  =  6. 


i) 


I   .    I 


FIG.  65. — Flux  circling  a  full-pitch  multiple  coil  during  short-circuit. 

Let  (f>s  be  the  number  of  lines  of  force  that  circle  1  in.  length  of 
the  slot  part  of  the  coil  M  for  each  ampere  conductor 
in  the  group  of  conductors  that  are  simultaneously  under- 
going commutation. 

and  (j)e  the  number  of  lines  of  force  that  circle  1  in.  length  of  the 
end  connections  of  the  coil  M  for  each  ampere  conductor 
in  the  group  of  end  connections  that  are  simultaneously 
undergoing  commutation. 

In  one  of  the  slots  A  there  are  2T  conductors,  each  carrying  a 
current  i,  so  that  the  flux  that  circles  one  side  of  coil  M  =  <f>8X 
Lcx2Txi  lines.  In  one  of  the  groups  of  end  connections,  as  at 
X,  Fig.  65,  there  are  T  conductors,  each  carrying  a  current  i,  so 


80  ELECTRICAL  MACHINE  DESIGN 

that  the  flux  that  circles  one  group  of  end  connections  of  length 
Le  =  (j)eXLexTxi  lines. 

The  total  flux  that  circles  the  coil  M  due  to  the  current  i  in  the 
coil  =  <f>c 

=  2Ti 


and  (L  +  M)=XW~8  henry 

=  2  T2  (2<j>sLc  +  <j>eLe}  XlO-8  henry 

Tc,  the  time  of  commutation,  is  the  time  taken  by  the  commuta- 
tor to  move  through  the  distance  of  the  brush  width  and  is  equal 

60  segments  covered  by  the  brush 

t/o  x  ' 


r.p.m.     total  number  of  commutator  segments 

60        segments  covered  by  the  brush 

X 


r.p.m.  S 

therefore,  when  the  brush  covers  only  one  segment,  the  average 

27* 
reactance  volt  age  =  ^= 


_97 

60 

66.  The  Effect  of  Wide  Slots  and  Brushes.  —  Neglect  for  the 
present  the  effect  of  the  end  connection  flux,  which  is  small  com- 
pared with  the  slot  flux,  and  compare  the  four  cases  shown  in 
Fig.  66. 
A  shows  part  of  a  winding  which  has  6  coil  sides  per  slot  and  a 

brush  which  covers  1  commutator  segment. 
B  shows  part  of  a  winding  which  has  2  coil  sides  per  slot  and  a 

brush  which  covers  1  commutator  segment. 
C  shows  part  of  a  winding  which  has  6  coil  sides  per  slot  and  a 

brush  which  covers  3  commutator  segments. 
D  shows  part  of  a  winding  which  has  2  coil  sides  per  slot  and  a 

brush  which  covers  3  commutator  segments. 

The  slots  in  cases  A  and  C  are  three  times  as  wide  as  those  in 
B  and  D  and  the  coils  shown  black  are  those  which  are  under- 
going commutation. 

In  B  the  time  of  commutation  is  the  same  as  in  A,  but  the 
flux  <J>a  is  three  times  as  large  since  the  reluctance  of  its  path  is 

proportional  to  the  ratio  -1—  -  —  ^rr,  the  reluctance  of  the  iron 

slot  width' 

part  of  the  path  being  neglected.     The  reactance  voltage  is 
therefore  three  times  as  large. 


COMMUTATION 


81 


In  C  the  time  of  commutation  is  three  times  as  long  as  in  A, 
and  the  flux  (f>s  also  is  three  times  as  large  since  there  are  three 
times  as  many  conductors  undergoing  commutation  at  the  same 
instant.  The  reactance  voltage  is  therefore  the  same  in  each 
case. 

In  D  the  time  of  commutation  is  the  same  as  in  C  and  so  also  is 
the  flux  (f>s,  since  the  reluctance  of  three  short  paths  in  series  is 
the  same  as  that  of  a  single  path  three  times  as  long.  The 
reactance  voltage  is  therefore  the  same  in  D  as  it  is  in  C  or  A. 


in 


1-1 1 


FIG.  66. — Effect  of  slot  and  brush  width  on  the  reactance  voltage. 

From  the  above  discussion  the  following  conclusions  can  be 
drawn — namely,  that  when  the  brush  covers  one  commutator 
segment  only,  the  reactance  voltage  is  greater  the  narrower  the 
slot;  compare  for  example,  cases  A  and  B'}  also  that  an  increase 
in  the  brush  width  has  no  effect  on  the  reactance  voltage  as  long 
as  the  group  of  conductors  simultaneously  commutated  is  not 
greater  than  the  total  number  of  conductors  per  slot  (compare 
A  and  C),  but  decreases  the  reactance  voltage  if  the  group  of 


82 


ELECTRICAL  MACHINE  DESIGN 


conductors  simultaneously  commutated  is  greater  than  the  total 
number  of  conductors  per  slot  (compare  B  and  D)  . 

The  method  for  determining  the  brush  width  is  taken  up  in 
Art.  72;  it  is  pointed  out  here,  however,  that  the  brush  generally 
covers  more  than  one  commutator  segment,  and  under  these 
conditions  the  case  of  a  very  narrow  slot  with  the  brush  covering 
one  commutator  segment,  namely  case  5,  Fig.  66,  can  be  neglected; 
with  this  restriction  the  formula  for  reactance  voltage  on 
page  80  can  be  used  for  all  slot  and  brush  widths. 

xlt  has  been  found  experimentally  that,  for  the  shape  of  coil 
in  general  use  in  D.-C.  machines  and  for  slots  which  have  the 

slot  depth  ,         .  .  ,    .  .    .  . 

ratio  -,—  :  —  ^ru=3.5,  a  value  which  is  seldom  exceeded  in  non- 
slot  width 

interpole  machines,  the  value  of  (f>s  may  be  taken  as  10  lines  per 
ampere  conductor  per  inch  length  of  core,  and  (f)e  may  be  taken 
as  2  lines  per  ampere  conductor  per  inch  length  of  end  connection. 
By  substituting  the  above  values  in  the  formula  for  reactance 
voltage  on  page  80,  the  following  result  is  obtained  for  the  reactance 
voltage  of  a  full  pitch  double  layer  multiple  winding  namely: 
Average  reactance  voltage 


(9) 


60 

=  1.33x£Xr.p.m.X/cXT2(Lc+0.1Le)10 


-8 


1,1,1 


FIG.  67. — Flux  circling  a  short-pitch  multiple  coil  during  short-circuit. 

67.  Short  Pitch  Multiple  Windings. — It  was  pointed  out  in  Art. 
15,  page  15,  that,  when  a  short-pitch  winding  is  used,  the  con- 
ductors of  the  coils  which  are  short  circuited  at  any  instant  are 
not  in  the  same  slot,  thus  Fig.  67  shows  the  short  pitch  diagram 

1  Hobart,  Continuous  Current  Dynamo  Design,  page  108. 


COMMUTATION  83 

which  corresponds  to  the  full-pitch  one  shown  in  Fig.  65,  and  it 
will  be  seen  that,  while  the  end  connection  flux  is  the  same  in 
each  case,  the  slot  flux  <£s  has  only  half  the  value  for  a  short- 
pitch  winding  that  it  has  for  a  full-pitch  winding  so  long  as  the 
pitch  is  short  enough  to  prevent  the  conductors  which  are  short- 
circuited  at  any  instant  from  lying  in  the  top  and  bottom  of  the 
same  slot. 

For  a  short -pitch  double-layer  multiple  winding  the  value  of  the 
average  reactance  voltage 

.          (10) 


FIG.  68. — Coils  in  a  series  winding  that  are  short-circuited  by  one  brush. 

68.  Calculation  of  the  Reactance  Voltage  for  Machines  with 
Series  or  Two  Circuit  Windings. — Fig.  68,  which  is  a  reproduction 
of  Fig.  21,  shows  that  when  only  one  +  and  one  —  brush  are 

used  each  brush  short  circuits  ^  coils  in  series,  so  that  the  average 
reactance  voltage  in  such  a  case 

When,  however,  the  same  number  of  sets  of  brushes  are  used  as 
there  are  poles,  so  that  brushes  are  also  placed  at  b  and  c,  there  is 
a  short  commutation  path  round  one  coil  which  is  short-circuited 
by  two  brushes  at  the  same  potential,  in  addition  to  the  long 

path  around  ~  coils  in  series  and,  so  far  as  this  short  path  alone  is 

concerned,   the   average  reactance  voltage 

=  1.33  x£Xr.p.m.X/cxr2(Lc +  0.1  Le)10-8. 


84  ELECTRICAL  MACHINE  DESIGN 

The  value  of  the  reactance  voltage  that  should  be  used  as 
a  criterion  for  commutation  is  somewhere  between  these  two 
values,  and  the  results  are  still  further  complicated  by  what  is 
known  as  selective  commutation  which  was  described  in  Art.  17, 
page  19,  so  that  in  practice  it  is  usual  to  use  the  former  of  the 
two  equations,  which  is  pessimistic;  the  commutation  will  gener- 
ally be  about  20  per  cent,  better  than  that  indicated  by  the  value 
of  reactance  voltage  so  found. 

69.  Formulae  for  Reactance  Voltage.  —  Collecting  together  the 
results  obtained  in  Arts.  66,  67  and  68,  the  following  formulae  are 
obtained: 

The  average  reactance  voltage 

=  1.33xSXr.p.m.X/cxr2(Z/c  +  0.1   Le)10~8  for  full-pitch  mul- 
tiple windings 

=  1.33  XSXr.p.m.X/c  X  T2  (^  +  0.1  Le)  10~8  for  short-pitch  mul- 
tiple windings 
=  1.33  X/SXr.p.m.  X  /c  X  T2  (Lc  +  0.1   Le)  |  X  10~8    for    series 

windings. 

It  is  pointed  out  in  Art.  99,  page  117,  that,  in  order  to  have 
an  economical  machine,  the  core  length  Lc  should  lie  between  the 
values  (0.9  to  0.6)  X[pole  pitch]. 

The  length  Le  of  the  end  connections  is  directly  proportional 
to  the  pole  pitch  and  =1.4  (pole  pitch)  approximately,  so  that 
Le  has  a  value  between  (1.6  and  2.4)  X[LC]  and  an  average  value 
=  2LC. 

Substituting  this  average  value  in  the  above  formula  for  react- 
ance voltage  the  following  approximate  formula  is  obtained: 
The  average  reactance  voltage 

10~8  (12) 


where        S   =  the  number  of  commutator  segments 

r.p.m.  =the  speed  of  the  machine  in  revolutions  per  minute 
7c  =  the  current  in  each  armature  conductor 
jT  =  the  number  of  turns  per  coil 
Lc  =  the  frame  length  in  inches 

—  =  1  for  multiple  and  =  ^  for  series  windings 
paths  2 

A;  =  1.6  for  series  and  full-pitch  multiple  windings 
=  0.93  for  short-pitch  multiple  windings. 


CHAPTER  IX 
COMMUTATION   (Continued) 

70.  The  Sparking  Voltage. — Down  to  this  point  it  has  been 
assumed  that  the  coils  in  which  the  current  is  being  commutated 
are  in  such  a  position  between  the  poles  that,  during  commuta- 
tion, they  are  not  cutting  any  lines  of  force  due  to  the  m.m.f.  of 
the  field  and  the  armature.  Under  these  conditions  the  value 
of  the  reactance  voltage  when  sparking  begins  is  called  the 
sparking  voltage,  and  depends  on  the  brush  resistance,  as  shown 
in  Art.  61,  page  76. 

In  practice  the  brushes  are  generally  shifted  from  the  above 
neutral  position  in  such  a  direction  that  the  coils  which  are 
undergoing  commutation  are  in  a  magnetic  field,  and  an  e.m.f. 
Es  is  generated  in  them,  due  to  the  cutting  of  this  field,  which 
opposes  the  e.m.f.  of  self  and  mutual  induction  and  so  causes  the 
commutation  to  be  more  nearly  perfect.  In  such  cases  the 
value  of  the  resultant  of  this  generated  voltage  and  of  the  react- 
ance voltage,  when  sparking  begins,  is  called  the  sparking  voltage. 

As  the  load  on  a  machine  increases  the  reactance  voltage 
jncreases  with  it,  and  in  order  that  the  commutation  may  be 
perfect  at  all  loads  the  voltage  Es  must  increase  at  the  same  rate; 
this  can  only  be  the  case  if  the  distance  the  brushes  are  shifted 
from  the  neutral  varies  with  the  load. 

Suppose  that  the  brushes  are  in  such  a  position  that  commuta- 
tion is  perfect  at  50  per  cent,  overload,  and  that  they  are  fixed 
there;  then  at  no-load  there  will  be  no  reactance  voltage  to 
counteract,  but  there  will  be  a  large  generated  voltage  Es  which 
will  cause  a  circulating  current  to  flow  in  the  short-circuited  coil, 
and  sparking  will  take  place  if  Es  is  larger  than  the  sparking 
voltage. 

Modern  D.-C.  machines  are  expected  to  carry  any  load  from 
no-load  up  to  25  per  cent,  overload  without  sparking  and  also 
without  shifting  of  the  brushes  during  operation.  To  accom- 
plish this  result  the  brushes  are  shifted  from  the  neutral  position, 
in  such  a  direction  as  to  help  commutation  when  the  machine  is 
loaded,  until  the  machine  is  about  to  spark  at  no-load;  the 
voltage  ES)  which  is  generated  in  the  short-circuited  coil,  will  then 

85 


86 


ELECTRICAL  MACHINE  DESIGN 


be  a  little  less  than  the  sparking  voltage.  When  the  machine  is 
carrying  25  per  cent,  overload  the  reactance  voltage  will  be 
greater  than  the  generated  voltage  Es  by  an  amount  which  is 
just  a  little  less  than  the  sparking  voltage,  and  half  way  between 


Volts 


Shunt 


Volts 


Curve 


Compound 


Load 


Volts 


B 


Load 
Over  Compound 

FIG.  69. — Variation  of  the  voltage  in  the  short-circuited  coil  with  load. 

these  two  points  Es  will  be  equal  and  opposite  to  the  reactance 
voltage  and  the  commutation  will  be  perfect. 

From  the  above  it  would  seem  that  the  reactance  voltage  at 
25  per  cent,  overload  could  have  a  value  equal  to  about  twice  the 
sparking  voltage,  but  in  obtaining  this  result  it  has  been  assumed 


COMMUTATION  87 

that  the  generated  voltage  E8  remains  constant  at  all  loads;  as  a 
matter  of  fact,  it  decreases  with  increase  of  load  due  to  the  cross- 
magnetizing  effect  of  the  armature,  as  pointed  out  in  Art.  48, 
page  54.  To  prevent  this  decrease  in  the  value  of  E8  from 
becoming  too  large,  the  relation  between  the  field  and  armature 
strengths  is  fixed  by  making  the  field  ampere-turns  per  pole  for 
gap  and  tooth  greater  than  1.2  (the  armature  ampere-turns  per 
pole)  +  the  demagnetizing  ampere-turns  per  pole;  see  Art.  52, 
page  61. 

The  diagrams  in  Fig.  69  show  the  variation  of  E8  and  of  the 
reactance  voltage  with  load.  Curve  1  shows  the  relation  between 
E8  and  the  load,  and  curve  2  shows  that  between  the  reactance 
voltage  and  load.  The  brushes  are  shifted  until  the  value  of  Es 
at  no-load  is  equal  to  the  sparking  voltage;  at  load  B  the  com- 
mutation is  perfect,  and  at  load  C  the  reactance  voltage  is  greater 
than  E8  by  the  sparking  voltage.  These  curves  show  clearly 
the  superiority  of  the  overcompound  machine  as  far  as  commu- 
tation is  concerned. 

71.  Minimum  Number  of  Slots  per  Pole. — Fig.  70  shows  three 
of  the  stages  in  the  commutation  of  the  current  in  a  machine 
which  has  six  coil  sides  per  slot.  The  commutator  segments  are 
evenly  spaced,  while  the  coils,  being  in  slots,  are  not.  It  will  be 
seen  that,  between  the  instant  when  the  brush  breaks  contact 
with  coil  A  and  the  instant  when  it  breaks  contact  with  coil  C, 
the  slot  in  which  these  coils  lie  has  moved  through  the  distance 
x,  so  that,  if  the  magnetic  field  in  which  the  coils  undergo  com- 
mutation is  just  right  for  coil  A,  it  will  be  a  little  too  strong 
for  coil  J5,  and  much  too  strong  for  coil  C;  this  latter  coil  will  there- 
fore be  so  badly  commutated  that  sparking  will  result  and  will 
show  up  on  the  commutator  in  the  blackening  of  every  third 
commutator  segment  due  to  the  poor  commutation  of  the  coil 
to  which  it  is  connected.  The  distance  x  =  the  slot  pitch  —  width 
of  one  commutator  segment. 

The  distance  through  which  a  slot  moves  while  the  conductors 
which  it  carries  are  undergoing  commutation  is  limited  by  making 
the  number  of  slots  per  pole  such  that  there  are  not  less  than  3.5 
slots  in  the  space  between  the  poles;  this  space  is  generally  30 
per  cent,  of  the  pole  pitch,  so  that  the  number  of  slots  per  pole, 
corresponding  to  3.5  slots  in  the  space  between  poles,  is  12,  and  is 
the  smallest  number  of  slots  per  pole  that  should  be  used.  For 
large  machines  there  are  seldom  less  than  14  slots  per  pole. 


88 


ELECTRICAL  MACHINE  DESIGN 


72.  The  Brush  Width. — It  was  pointed  out  in  Art.  66,  page  82, 
that  the  brush  width  has  very  little  effect  on  the  reactance 
voltage  because,  while  the  number  of  adjacent  coils  that  are 
simultaneously  undergoing  commutation  increases  with  the  brush 
width,  the  time  of  commutation  also  increases  at  the  same  rate. 

Figure  71  shows  the  distribution  of  the  magnetic  field  in  the 
space  between  the  poles  of  a  loaded  D.-C.  generator  and  also  the 


u 


FIG.  70. — Variation  of  the  position  of  the  short-circuited  coil  when  there 
are  several  coils  per  slot. 

position  of  a  wide  brush.  It  will  be  seen  that,  in  order  to  keep 
the  tip  a  of  the  brush  from  under  the  pole,  where  the  magnetic 
field  is  too  strong ,  the  tip  b  has  to  be  in  a  magnetic  field 
which  is  not  a  reversing  field,  so  that  at  the  start  of  commutation 
in  any  coil  the  current  in  that  coil  will  increase,  as  shown  in  Fig.  72, 
and  the  effective  time  of  commutation  will  be  less  than  the 


COMMUTATION 


89 


cd 

apparent  time  in  the  ratio  —     To  limit   this  effect  the  brush 

ce 

should  not  cover  more  than  28  per  cent,  of  the  space  between  poles 
or  0.28X0.3  times  the  pole  pitch. 

The  brush  arc  measured  on  the  armature  surface  should  there- 


FIG.  71. — Flux  distribution  at  full-load  in  the  space  between  poles. 


e  d       c 

FIG.  72. — Variation  of  the  current  in  the  short-circuited  coil  when  the  biush 

is  too  wide. 

pole  pitch 

fore  not  be  greater  than  -  —^^ or>  measured  on  the  commu- 
tator surface,  should  not  be  greater  than 

pole  pitch     dia.  commutator 


12 


X 


dia.  armature 


There  is  still  another  limit  to  the  brush  arc.  When  the  brushes 
are  shifted  from  the  neutral  position  in  order  to  help  commutation 
under  load  there  is  an  e.m.f.  generated  in  the  short-circuited 
coils,  namely  Es.  Thus,  in  the  case  shown  in  Fig.  73,  where  the 
brush  covers  five  segments,  the  voltage  generated  between  a  and 
b  is  that  of  five  coils  in  series  and  the  resistance  of  the  path  to  the 


90 


ELECTRICAL  MACHINE  DESIGN 


circulating  current  that  will  flow  is  comparatively  low,  being 
that  of  one  coil  and  two  contacts.  To  prevent  trouble  due  to 
this  circulating  current  it  is  necessary  to  limit  the  brush  arc  so 
that  it  shall  not  cover  more  than  three  commutator  segments. 

73.  Limits  of  the  Reactance  Voltage. — In  the  discussion  in 
Art.  61,  page  76,  it  is  shown  that  the  reactance  voltage  should 
not  exceed  the  voltage  drop  across  one  brush  contact  when  the 
brushes  are  in  such  a  position  that  the  short-circuited  coil  is  not 


FIG.  73. — Circulating  currents  at  no-load  in  a  wide  brush. 


cutting  any  lines  of  force  due  to  the  m.m.f.  of  the  field  and 
armature,  and  the  discussion  in  Art.  70,  page  85,  shows  that 
higher  values  may  be  used  when  the  brushes  are  shifted  forward 
so  as  to  help  commutation. 

Experiment  shows  that  higher  values  of  the  reactance  voltage 
may  be  used  than  the  limits  indicated  by  theory  and  the  follow- 
ing, found  from  experience,  may  be  used  in  design  work. 

For  machines  which  must  operate  without  destructive  sparking 
at  all  loads  from  no-load  to  25  per  cent,  overload  with  brushes  in 
a  fixed  position,  the  reactance  voltage  at  full  load  should  not 
exceed  0.7  (volts  drop  per  pair  of  brushes)  with  the  brushes  on 
the  neutral  position,  nor  should  it  exceed  the  volts  drop  per 
pair  of  brushes  for  machines  with  the  brushes  shifted  so  as  to 
help  commutation. 

These  figures  apply  to  machines  which  are  built  so  that: — 
The  number  of  slots  per  pole  is  greater  than  12; 


COMMUTATION  91 

The  brush  arc  covers  less  than  1/12  of  the  pole  pitch  when 

measured  on  the  armature  surface>  and  also  does  not  cover 

more  than  three  commutator  segments; 

The  pole  arc  is  not  greater  than  70  per  cent,  of  the  pole  pitch; 
ATg  +  t  is  greater  than  1.2  (armature  AT  per  pole)  +  the  demag- 
netizing AT  per  pole. 

These  figures  are  intimately  connected  with  one  another  and 
also  with  the  reactance  voltage;  for  example,  the  brushes  may  be 
made  wider  and  the  main  field  weaker  than  indicated,  but  in 
such  cases  the  reactance  voltage  must  also  be  decreased  otherwise 
trouble  will  develop. 

In  addition  it  must  be  noted  that,  as  pointed  out  in  Art.  68, 
page  84,  the  commutation  of  a  machine  with  a  series  winding  is 
about  20  per  cent,  better  than  represented  by  the  value  of  the 
reactance  voltage  obtained  from  the  formula. 

For  machines  with  short-pitch  windings  on  the  other  hand,  the 
operation  is  about  30  per  cent,  worse  than  represented  by  the 
value  of  the  reactance  voltage  obtained  from  the  formula,  because, 
as  shown  in  Art.  15,  page  15,  the  effective  width  of  the  space 
between  poles  is  less  than  the  actual  width  by  the  distance  of 
one  slot  pitch. 


FIG.  74. — Field  due  to  the  armature  m.m.f. 

74.  Limit  of  Armature  Loading. — Fig.  74  shows  part  of  a 
multipolar  machine;  the  current  in  the  armature  conductors  is 
represented  by  crosses  and  dots  and  the  lines  of  force  of  armature 
reaction  are  also  shown.  As  the  number  of  armature  ampere- 
turns  per  pole  increases  the  field  ampere-turns  per  pole  must  also 
be  increased  so  as  to  prevent  too  great  a  distortion  of  the  main 
field  and  consequently  poor  commutation. 

There  is,  however,  one  part  of  the  armature  field  which  is  not 
counteracted  by  the  main  field,  namely,  the  field  out  on  the  end 
connections;  this  is  stationary  in  space  and  therefore  cut  by  the 
coils  which  are  undergoing  commutation.  The  e.m.f.  due  to  the 
cutting  of  this  field  acts  in  such  a  direction  as  to  oppose  commuta- 
tion, and  in  order  to  prevent  this  voltage  from  having  such  a 


92 


ELECTRICAL  MACHINE  DESIGN 


value  as  to  cause  trouble  it  is  advisable  to  limit  the  number  of 
armature  ampere-turns  per  pole  to  about  7500;  a  higher  value 
than  this  must  be  accompanied  by  a  low  reactance  voltage 
otherwise  trouble  will  develop. 

75.  Interpole  Machines. — -It  was  pointed  out  in  Art.  70,  page 
85,  that  commutation  can  be  helped  by  shifting  the  brushes  so 
that  the  short-circuited  coils  are  in  a  magnetic  field,  and  it  was 
also  shown  that,  if  the  e.m.f.  generated  due  to  this  field  was  to  be 
equal  and  opposite  at  all  times  to  the  reactance  voltage,  the 
strength  of  the  field  should  be  proportional  to  the  load. 


FIG.  75. — Magnetic  circuit  of  a  four-pole  interpole  machine. 

Figure  75  shows  an  interpole  generator  diagrammatically; 
n  and  s  are  auxiliary  poles  which  have  a  series  winding,  so 
that  their  strength  increases  as  the  load  increases.  In  a  generator 
the  brushes  would  be  shifted  forward  in  the  direction  of  motion 
so  that  B+  would  come  under  the  tip  of  the  N  pole  and  B_ 
under  the  tip  of  the  S  pole;  instead  of  that,  in  the  interpole 
machine,  the  auxiliary  n  pole  is  brought  to  the  brush  B+  and  the 
auxiliary  s  pole  to  the  brush  #_. 

Before  the  interpole  can  send  a  flux  across  the  air  gap  in  such 
a  direction  as  to  help  commutation  it  must  have  a  m.m.f.  equal 
to  that  of  the  cross  magnetizing  effect  of  the  armature  which 

r7 

=  J—  /C  ampere-turns,  see  Art.  48,  page  55, 
=  the  armature  ampere-turns  per  pole, 


COMMUTATION  93 

and  in  addition  a  m.m.f.  to  send  a  flux  across  the  air  gap  large 
enough  to  generate  an  e.m.f.  in  the  short-circuited  coil  which  shall 
be  equal  and  opposite  to  the  e.m.f.  of  self  and  mutual  induction 
and  to  that  generated  due  to  cutting  the  magnetic  field  out  on 
the  end  connections. 

In  order  that  the  flux  produced  by  the  interpole  may  be  always 
proportional  to  the  load,  it  is  necessary  that  the  interpole  magnetic 
circuit  do  not  become  saturated. 

76.  Interpole  Dimensions. — Wtp,  the  interpole  arc,  should 
be  such  that,  while  the  current  in  a  conductor  is  being  commu- 
tated,  the  slot  in  which  that  conductor  lies  is  under  the  interpole. 


FIG.  76. — Dimensions  of  interpole. 

The  distance  moved  by  the  coil  A,  Fig.  70,  while  it  is  short- 
circuited  by  the  brush,  is  equal  to  the  brush  arc  referred  to 

armature  diameter 

the  armature  surf  ace  =  brush  arc  X  — - p —      — ; 

commutator  diameter' 

the  total  arc  which  must  be  under  the  influence  of  the  interpole  is 
greater  than  this  by  the  distance  x  which,  as  pointed  out  in  Art. 
71 ,  page  87,  =the  slot  pitch  --  the  width  of  one  commutator 
segment  referred  to  the  armature  surface. 

As  shown  in  Fig.  76,  the  flux  fringes  out  from  either  side 
of  the  interpole  by  a  distance  which  is  approximately  equal 
to  the  air-gap  clearance,  so  that  the  effective  interpole  arc 
=  Wip  +  2d;  this  arc  must  be  equal  to  the  slot  pitch  + 
brush  arc  —  segment  width,  all  referred  to  the  armature  surface. 

This  arc  must  also  be  such  that  the  reluctance  of  the  gap 
under  the  interpole  shall  vary  as  little  as  possible  for  different 
positions  of  the  armature,  otherwise  the  interpole  field  will 
be  a  pulsating  one;  if,  for  example,  the  arc  were  equal 
to  the  width  of  one  tooth,  then- the  interpole  air-gap  reluctance 
would  vary  from  a  maximum  when  a  tooth  was  under  the  pole 
to  a  minimum  when  a  slot  was  under  the  pole.  If  the  interpole 
effective  arc  be  a  multiple  of  the  slot  pitch,  as  in  Fig.  76,  where 
it  is  equal  to  twice  the  slot  pitch,  the  reluctance  of  the  gap  will 


94  ELECTRICAL  MACHINE  DESIGN 

be  practically  constant,  because,  as  one  tooth  moves  from  under 
the  pole  another  comes  under  its  influence. 

As  a  general  rule  the  effective  interpole  arc  is  about  15  per  cent 
of  the  pole  pitch  and  is  adjusted  so  as  to  be  approximately  a 
multiple  of  the  slot  pitch;  the  brush  arc  is  then  made  to  suit  the 
interpole  arc  so  found.  To  allow  space  for  the  interpole  and  to 
prevent  the  interpole  leakage  flux  from  being  too  large,  the  arc 
of  the  main  pole  is  kept  down  to  about  65  per  cent  of  the  pole 
pitch. 

The  axial  length  of  the  interpole,  Lip,is  found  as  follows:  If 
Bi  is  the  average  interpole  gap  density,  then  the  voltage  gene- 
rated in  each  coil  while  under  the  interpole 

=  the  lines  cut  per  second  XlO~8 

=  2 


and  this  should  equal  the  reactance  voltage,  which,  for  a  full  pitch 
winding,  the  type  used  on  interpole  machines, 

=  1.6xSXr.p.m.  X/cXl/cX  r2XlO~8volts  per  coil; 
therefore,  equating  these  two  values  together  and  simplifying 


=  ampere  conductors  per  inch  X  Lc  X  48 

r       ,     /ampere  conductor  per  inch\ 
and  Li  =  Lc  I-  -\  X  48 

The  value  of  Bi  is  generally  chosen  about  45,000  lines  per  square 
inch  at  full  load,  for  which  value  the  interpole  circuit  does  not 
become  saturated  up  to  50  per  cent,  overload. 

The  value  of  ampere  conductors  per  inch  seldom  exceeds  900; 
for  this  value,  and  for  the  value  of  interpole  gap  density  given 
above 


The  interpole  excitation  is  not  figured  out  accurately;  the  usual 
practice  is  to  put  on  each  interpole  a  number  of  ampere-turns 
which  at  full  load  =1.5  (armature  AT  per  pole) 

=  1.5 

such  a  value  is  sufficient  to  overcome  the  armature  m.m.f.  and  also 
to  send  sufficient  flux  across  the  interpole  gap  to  allow  the  neces- 
sary voltage  to  be  generated.  This  value  of  m.m.f.  is  generally 


COMMUTATION 


95 


too  large  and  the  final  adjustment  is  made  by  means  of  a  shunt 
after  the  machine  has  been  erected. 

77.  Flashing  Over. — If  the  voltage  between  adjacent  commu- 
tator segments  becomes  too  high  the  machine  is  liable  to  flash 
over  on  the  commutator  from  brush  to  brush,  particularly  if  the 
commutator  is  dirty.  The  voltage  between  two  adjacent  bars 
should  not  if  possible  exceed  40;  turbo  generators  have  been 
built  in  which  this  value  was  greater  than  60,  but  such  machines 
are  sensitive  to  changes  of  load  and  liable  to  flash  over  unless 
supplied  with  compensating  windings.  It  must  be  clearly  under- 
stood that  there  is  considerable  difference  between  the  maximum 
voltage  between  commutator  bars  and  the  average  value,  this 
can  be  seen  from  Fig.  49,  which  shows  that  when  the  machine  is 
loaded  the  flux  density  in  the  air  gap  at  point  d  is  much  higher 
than  the  average  gap  density;  at  this  point  the  highest  voltage 
per  coil  will  be  generated. 


A  B 

FIG.  77. — Armature  field  with  and  without  compensating  windings. 

Flashing  over  is  generally  caused  by  a  sudden  change  of  load, 
the  reason  being  as  follows:  Fig.  77,  diagram  A,  shows  the  arma- 
ture cross  field  when  the  machine  is  loaded;  a  sudden  change  in 
load  causes  the  value  of  this  field  to  change  and  a  voltage  is 
generated  in  the  armature  coils  which  is  proportional  to  the  rate 
of  change  of  flux  and  is  a  maximum  in  the  coil  a.  This  voltage 
increases  or  decreases  that  which  already  exists  between  adja- 
cent commutator  segments  and  the  increase  may  be  sufficient  to 
cause  the  voltage  between  adjacent  commutator  segments  to 
become  too  high  and  the  machine  to  flash  over. 

When  the  load  is  very  fluctuating  in  character,  such  as  the 
load  on  a  motor  driving  a  reversing  rolling  mill  at  the  instant  of 
reversal  of  the  rolls,  at  which  instant  the  current  changes  from 


96 


ELECTRICAL  MACHINE  DESIGN 


less  than  full-load  current  to  about  three  times  full-load  current 
in  the  opposite  direction,  the  average  voltage  between  commuta- 
tor bars  should  not  exceed  15,  or  it  will  be  necessary  to  supply 
the  machine  with  a  compensating  winding  to  prevent  flashing 
over.  Fig.  78  shows  such  a  machine.  The  poles  carry  a 
winding  on  the  pole  face  which  is  connected  in  series  with  the 


FIG.  78. — Yoke  of  machine  with  interpoles  and  compensating  windings. 

armature  and  which  has  the  same  number  of  ampere-turns  per 
pole  as  there  are  on  the  armature.  The  current  in  the  pole-face 
conductors  passes  in  the  opposite  direction  to  that  in  the  arma- 
ture conductors  under  the  same  pole,  so  that  the  armature  field 
is  completely  neutralized,  as  shown  in  Fig.  77,  diagram  B;  there 
is  no  crowding  of  the  lines  into  one  pole  tip  as  shown  in 
Fig.  49,  and  there  is  no  sudden  change  of  armature  field  with 
load  and  therefore  no  tendency  to  flash  over.  » 


CHAPTER  X 

EFFICIENCY  AND  LOSSES 

_0    ,™     ^^  .  .  output  output 

78.  The  Efficiency  of  a  generator  =  -T— 

input      output  +  losses 

,  output     input  -losses    , 

and  that  of  a  motor  =  ^  —  —  =  —        —where   the    losses 

input  input 

are: 

Mechanical  losses  —  windage,  brush  and  bearing  friction. 
Iron  losses  —  hysteresis  and  eddy  current  losses. 
Copper  losses  in  field  and  armature  coils. 
Commutator  contact  resistance  loss. 

79.  Bearing  Friction.  —  In   a  high   speed   bearing   with   ring 
lubrication  there  is  always  a  film  of  oil  between  the  shaft  and  the 
bushing;  bearing  friction  is  therefore  an  example  of  fluid  friction 
and  the  tangential  force  at  the  rubbing  surface  in  such  a  case  = 
kAbVbn  lb.,  where  A;  is  a  constant  which  depends  on  the  vis- 
cosity of  the  oil  and  is  found  by  experiment  to  be  =0.036  for 
bearings  with  ring  lubrication  using  light  machine  oil. 

Ab  is  the  projected  area  of  the  bearing  in  square  inches 
=  (the  bearing  diameter  db  in  inches  X  the  bearing  length 
lb  in  inches); 

Vb  is  the  rubbing  velocity  of  the  bearing  in  feet  per  minute; 

n  is  found  experimentally  to  vary  from  1  for  low  values  of  Vb 
to  0  for  very  high  values  and  is  approximately  —  0.5  for  bearing 
speeds  from  100  to  1000  ft.  per  minute. 

For  moderate  speed  bearings  with  ring  lubrication  and  with 
light  machine  oil  the  force  of  friction  =  0.036  AbVb*  pounds 
and  the  friction  loss  =  0.036AbVb*  ft.  lb.  per  minute 


=  0.  81  dblb~      watts.  (13) 


It  is  important  to  notice  that  this  loss  is  independent  of  the 
bearing  pressure  and  is  therefore  independent  of  the  load. 

As  the  pressure  on  the  bearing  increases  the  thickness  of  the 
oil  film  decreases  and  at  a  certain  limiting  pressure  it  breaks 
down   and   the   bearing   seizes.     For   electrical   machinery   the 
7  97 


98  ELECTRICAL  MACHINE  DESIGN 

bearing  load     .      .  . 
bearing  pressure  =—    —f-     —>  should  not  exceed  80  Ib.    per 

-Aft 

square  inch  when  the  machine  is  carrying  full  load,  such  a  bearing 
will  carry  100  per  cent,  overload  without  breakdown. 

The  bearing  loss  increases  rapidly  with  the  rubbing  velocity 
and  after  a  certain  velocity  has  been  reached  the  bearings  are  no 
longer  large  enough  to  be'  self-cooling.  For  self-cooling  bearings 
the  rubbing  velocity  should  not  exceed  1000  ft.  per  minute 
unless  the  bearing  is  specially  designed  to  get  rid  of  the  heat,  and 
even  this  value  should  only  be  used  for  machines  which  are  built 
so  that  a  large  supply  of  cool  air  passes  continuously  over  the 
external  surface  of  the  bearing.  The  bearings  of  totally  enclosed 
motors  for  example  are  poorly  ventilated  and  should  not  be  run 
with  a  rubbing  velocity  greater  than  about  800  ft.  per  minute. 

The  thickness  of  the  oil  film  in  a  bearing  varies  inversely  as  the 
temperature  of  the  oil,  and  this  temperature  should  not  exceed 
70°  C.  when  measured  by  a  thermometer  in  the  oil  well. 

80.  Brush  Friction.  —  If 
H  is  the  coefficient  of  friction; 
P  the  brush  pressure  in  pounds  per  square  inch; 
A  the  total  brush  rubbing  surface  in  square  inches; 
Vr  the  rubbing  velocity  in  feet  per  minute; 
then  the  friction  loss  =/j.PAVr  ft.  Ib.  per  minute. 

Approximate,  values  found  in  practice  are: 
fji  =  0.28  and  P  =2  Ib.  per  square  inch,  for  which  values  the 

friction  loss  =  1.25  A^.       watts.  (14) 


81.  Windage  Loss.  —  It  is  difficult  to  predetermine  this  loss, 
but,  up  to  peripheral  velocities  of  6000  ft.  per  minute,  it  is  so 
small  that  it  may  be  neglected.  Fig.  79  shows  the  windage  and 
bearing  friction  loss  of  a  motor  which  has  an  armature  diameter 
of  100  in.  and  three  bearings  each  10  in.  by  30  in.  The 
circles  show  the  actual  test  points  and  the  curve  shows  the 
value  of  the  bearing  friction  loss  calculated  from  the  formula, 

friction  loss  =3X0.81  X  db  X  h  *  watts.    At  a  speed  of  230 


r.p.m.  the  peripheral  velocity  of  the  armature  is  6000  ft.  per 
minute,  up  to  which  speed  the  windage  loss  can  be  neglected; 
at  higher  speeds  it  becomes  large  because  it  is  proportional  to 
the  (peripheral  velocity).3 


EFFICIENCY  AND  LOSSES 


Few  electrical  machines  except  turbo  generators  are  run  at 
peripheral  speeds  greater  than  6000  ft.  per  minute,  because  the 
cost  increases  very  rapidly  for  higher  speeds  on  account  of  the 


30 


20 


M 


100  200  300  400 

R.P.M. 

FIG.  79. — Windage  and  friction  loss  in  a  large  motor. 


special  construction  required  to  hold  the  coils  against  centrif- 
ugal force. 

82.  Iron  Losses. — It  may  be  seen  from  Fig.  80  that  the  flux  in 


FIG.  80. — Distribution  of  flux  in  the  armature. 

any  portion  of  the  armature  of  a  D.  C.  machine  goes  through  one 
cycle  while  the  armature  moves  through  the  distance  of  two 
pole  pitches;  that  is,  the  flux  in  any  portion  of  the  armature 


100  ELECTRICAL  MACHINE  DESIGN 

passes  through  ^  cycles  per  revolution,  or  through  ^X  — 

Zi  Z  OU 

cycles  per  second. 

The  iron  losses  consist  of  the  hysteresis  loss  which  =KBr*fW 
watts,   and  the  eddy  current  loss  which    =    Ke(Bft)2W  watts 
where  K  is  the  hysteresis  constant  and  varies  with  the  grade 
of  iron; 

Ke  is  a  constant  which  is  inversely  proportional  to   the 

electrical  resistance  of  the  iron; 

B  is  the  maximum  flux  density  in  lines  per  square  inch; 
/   is  the  frequency  in  cycles  per  second; 
W  is  the  weight  of  the  iron  in  pounds; 
t    is  the  thickness  of  the  core  laminations  in  inches. 

The  eddy  current  loss  can  be  reduced  by  the  use  of  iron  which 
has  a  high  electrical  resistance.  At  present,  however,  most  of  the 
grades  of  very  high  resistance  iron  have  a  lower  permeability 
than  those  of  lower  electrical  resistance;  they  also  cost  more  and 
are  more  brittle;  machines  built  with  such  iron  are  liable  to  have 
the  teeth  break  off  due  to  vibration.  The  reduction  in  the 
total  loss  by  the  use  of  high  resistance  iron  is  not  so  great  as 
one  would  expect,  because  a  large  part  of  the  loss  is  due  to  losses 
discussed  in  the  next  article  and  these  are  not  greatly  affected 
by  the  grade  of  iron  used. 

The  eddy  current  loss  can  be  reduced  by  a  reduction  in  t,  the 
thickness  of  the  laminations;  this  value  is  generally  about  0.014 
in.;  thinner  iron  is  difficult  to  handle. 

83.  Additional  Iron  Losses. — Besides  the  ordinary  hysteresis 
and  eddy  current  loss  already  mentioned  there  are  additional 
losses  which  cannot  be  calculated,  due  to  the  following  causes: 

(a)  Loss  due  to  filing  of  the  slots.  When  the  laminations 
that  form  the  core  have  been  assembled  it  will  be  found  that  in 
most  cases  the  slots  are  rough  and  must  be  filed  smooth  in  order 
that  the  slot  insulation  may  not  be  cut.  This  filing  burrs  the 
laminations  over  on  one  another  and  provides  a  low  resistance 
path  through  which  eddy  currents  can  flow;  that  is,  it  tends  to 
defeat  the  result  to  be  obtained  by  laminating  the  core. 

(6)  Losses  in  the  spider  and  end  heads  due  to  the  leakage  flux 
which  gets  into  these  parts  of  the  machine;  these  losses  may  be 
large  because  the  material  is  not  laminated. 

(c)   Loss  due  to  non-uniform  distribution  of  flux  in  the  arma- 


EFFICIENCY  AND  LOSSES  101 

ture  core.  When  calculating  the  value  of  Bc,  the  flux  density 
in  the  core,  page  45,  it  is  assumed  that  the  flux  ia  uniformly 
spread  over  the  core  area.  This  however  is  not  tife'QEfogantL 
the  actual  flux  distribution  is  shown  in  Fig.  80;  the  lines -of 
force  take  the  path  of  least  reluctance  and  there'! 9T3  -  crowd  in 
behind  the  teeth  until  that  part  of  the  core  becomes  saturated, 
then  they  spread  further  out.  Due  to  this  concentration  of 
flux,  the  core  loss,  which  is  approximately  proportional  to  (flux 
density),2  is  greater  than  that  got  by  assuming  that  the  flux 
distribution  is  uniform  through  the  whole  depth  of  the  core. 

It  is  sometimes  possible  to  increase  the  core  depth  so  as  to 
keep  the  apparent  flux  density  in  the  core  low  and  yet  make  no 
perceptible  reduction  in  the  core  loss,  because  the  increased  depth 
of  core  does  not  carry  its  proper  share  of  the  flux;  for  this 
reason  there  is  seldom  much  to  be  gained  by  making  the  value  of 
Bc  less  than  80,000  lines  per  square  inch,  which  is  near  the  point 
at  which  saturation  begins  and  the  flux  tends  to  become 
uniform. 

(d)  Pole  face  losses.     Fig.  39  shows  the  distribution  of  flux 
in  the  air  gap  of  a  D.  C.  machine  and,  as  the  armature  revolves 
and  the  teeth  move  past  the  pole  face,  e.m.fs.  will  be  induced 
which  will  cause  currents  to  flow  across  the  pole  face.     Experi- 
ment shows  that  when  solid  pole  faces  are  used  the  loss  due  to 
these  currents  increases  very  rapidly  as  the  slot  opening  becomes 
greater  than  twice  the  length  of  the  air  gap;  when  the  slot  open- 
ings are  wider  than  this  the  pole  face  must  be  laminated. 

(e)  Variation  of  the  iron  loss  with  load.     It  is  shown  in  Fig.  49 
that,  when  the  machine  is  loaded,  the  flux  density  is  not  uniform 
in  all  the  teeth  under  the  pole  but  is  stronger  at  one  pole  tip  than 
at  the  other.     The  effect  of  the  increase  of  flux  density  in  the 
teeth  under  one  pole  tip  in  increasing  the  iron  loss  is  greater  than 
the  effect  of  the  decrease  of  flux  density  in  the  teeth  under  the 
other  tip  in  reducing  the  iron  loss. 

84.  Calculation  of  Core  Loss. — Due  to  the  additional  losses 
it  is  impossible  to  predetermine  the  total  core  loss  by  the  use  of 
fundamental  formulae;  core  loss  calculations  for  new  designs  aie 
based  on  the  results  obtained  from  tests  on  similar  machines 
built  under  the  same  conditions.  Such  test  results  are  plotted 
in  Fig.  81  for  machines  built  with  ordinary  iron  .of  a  thickness 
of  0.014  in.,  the  slots  being  made  with  notching  dies  so  that  a 
certain  amount  of  filing  has  to  be  done. 


102 


ELECTRICAL  MACHINE  DESIGN 


Example  of  calculation:  For  the  machine  shown  in  Fig.  41  the  value  of 
B  at  the  actual  flux  density  in  the  teeth  and  Bc  the  average  flux  density  in 
the  bore  are  given  in  Art.  46,  page  49. 

$at  —  ISO'jGOO  lines  per  square  inch; 

Bf  <=84,OQO  lines  per  square  inch; 
Wt,  Sthe  to&tr* weight  of  the  armature  teeth  =  385  lb.; 
Wc,  the  total  weight  of  the  armature  core  =  2300  lb. ; 
The  frequency  =  16.6  cycles  per  second; 
The  loss  per  pound  for  the  teeth  =  6  watts,  from  Fig.  81; 
The  loss  per  pound  for  the  core  =  1.8  watts,  from  Fig.  81; 
The  total  loss  =  385X6 +  2300X1. 8  =  6450  watts. 


1015   20  25    30 


Cycles  per  Second 
40          50          50 


100 


10 


15 


35 


40 


20          25  3 

"V/atts-per  Lb. 
FIG.  81. — Iron  loss  curves  for  revolving  machinery. 


45 


50 


85.  Armature  Copper  Loss.  —  The  resistance  of  copper  at  the 
normal  operating  temperature  of  an  electric  machine  is  approxi- 
mately 1  ohm  per  circular  mil  cross-section  per  inch  length,  so 
that  if 

Z  is  the  total  number  of  conductors; 
Lb  is  the  length  of  one  conductor  in  inches; 
M  is  the  cross-section  of  each  conductor  in  circular  mils; 
7C  is  the  current  in  each  conductor  in  amperes; 

^r^ 
M 


then  the  resistance  of  one  conductor  in 


the  loss  in  one  conductor  in  watts  =irx/c2 

M 


EFFICIENCY  AND  LOSSES  103 

and  the  total  copper  loss  in  the  armature  in  watts  =  Z-^/c2     (15) 

The  value  of  L&  = 

1.35  (pole  pitch)  +  2  (armature  axial  length)  +  3  in. 
approximately  for  the  type  of  coil  shown  in  Fig.  33,  page  36. 

86.  Shunt  Field  Copper  Loss. — This  loss,  which  =  Etlf  watts, 
where  jE^is  the  terminal  voltage  of  the  machine  and  //  is  the 
current  in  the  shunt  coil,  is  made  up  of  the  loss  in  the  field  coils 
and  the  loss  in  the  field  rheostat;  the  latter  for  a  generator  is 
about  20  per  cent,  of  the  total  shunt  field  loss. 

87.  Series  Field  Copper  Loss. — This  loss  =Ia2Rs  watts,  where 
Rs  is  the  resistance  of  the  series  field  in  ohms  and  Ia  the  total 
armature  current.     When  a  series  shunt  is  used,  so  that  part  of 
the  current  Ia  passes  through  the  series  field  and  the  remainder 
passes  through  the  shunt,  the  resistance  Rs  is  the  combined  resist- 
ance of  the  series  field  and  the  series  shunt  in  parallel. 

88.  Brush  Contact  Resistance  Loss. — This  loss  has  already 
been  discussed  in  Art.  62,  page  76,  and  =EbIa  watts,  where  Eb 
is  the  voltage  drop  per  pair  of  brushes  and  Ia  is  the  armature 
current.     The  volts  drop  per  pair  of  brushes  is  approximately 
constant  over  a  wide  range  of  current,  as  shown  in  Fig.  64. 


CHAPTER  XI 


r 

T 


HEATING 

89.  Cause  of  Temperature  Rise. — The  losses  in  an  electrical 
machine  are  transformed  into  heat;  part  of  this  heat  is  dissipated 
by  the  machine  and  the  remainder,  being  absorbed,  causes  the 
temperature    of   the    machine    to   increase.     The    temperature 
becomes   stationary  when  the   heat   absorption  becomes   zero, 
that  is  when  the  point  is  reached  where  the  rate  at  which  heat  is 
generated  in  the  machine  is  equal  to  the  rate   at  which  it  is 
dissipated. 

90.  Maximum  Safe  Operating  Temperature. — The  highest  safe 
temperature  at  which  an  electrical  machine  can  be  operated 
continuously  is  about  85°  C.  with  the  present  practice  in  insu- 
lating, because,   if   subjected   to  that 
temperature    for   any  length  of  time, 
the    paper  and  cloth  which  are  used 
for  coil  insulation  become  brittle,  and 
pulverize  due  to  vibration. 

The  usual  heating  guarantee  is  that 
the  machine  shall  carry  full  load  con- 
-  tinuously  with  a  temperature  rise  of 
not  more  than  40°  C.  This  is  a  con- 
servative guarantee  and  allows  the 
machine  to  carry  25  per  cent,  overload 
without  injury  if  the  air  temperature 
does  not  exceed  25°  C. 

If  the  air  temperature  is  greater  than 

25°  C.  a  lower  temperature  rise  must 
FIG.    82.— The   heat    paths  be  allowed  in  order  that  the  final  tem. 

in  an  armature  core.  ,     ,,        .  , 

perature  shall  not  be  excessive. 

91.  Temperature  Gradient  in  the  Core  of  an  Electrical  Machine. 

—Fig.  82  shows  an  iron  core  built  up  of  laminations  that  are 
separated  from  one  another  by  varnish.  In  this  core  there  is 
an  alternating  magnetic  flux  and  the  loss  in  the  core  for  different 
flux  densities  and  for  different  frequencies  can  be  found  by  the 
help  of  the  curves  in  Fig.  81,  page  102. 

104 


B 


HEATING 


105 


The  hottest  part  of  the  core  is  at  A  and  the  heat  in  the  center 
of  the  core  has  to  be  conducted  to  and  dissipated  by  the  surfaces 
B  and  C. 

In  order  to  have  an  idea  as  to  the  relative  heat  resistances  of 
the  paths  from  A  to  the  surfaces  B  and  C,  consider  the  following 
propositions. 

(a)  Assume  that  all  the  heat  passes  in  the  direction  Y,  then 
the  watts  crossing  1  sq.  in.  of  the  core  at  y  =  (watts  per  cubic 
inch)  X  y  and  since  the  difference  in  temperature  between  two 


faces    a  distance  dy   apart  — 


(watts  per  cubic  inch)?/  dy 
1.5 


degrees 


centigrade,  where  1.5  is  the  thermal  conductivity  of  iron  in  watts 
per  1-in.  cube  per  1°  C.  difference  in  temperature,  therefore,  the 
difference  in  temperature  between  A  and  surface  B 


Temp. 


Temp. 


V  =  1000  Ft.  per  Min.  V  =  10,000  Ft.  per  Min. 

FIG.  83. — Temperatures  in  an  iron  core. 


Y 


=  Tab  = 


(watts  per  cubic  inch)?/  dy 


1.5 


Y2 


=  (watts  per  cubic  inch)  -=-  deg.  C. 

o 

(6)  If  the  heat  were  all  conducted  in  the  direction  X  then, 
since  the  conductivity  of  a  core  along  the  laminations  is  approxi- 
mately fifty-six  times  as  great  as  that  across  the  laminations  and 
layers  of  varnish,  the  difference  in  temperature  between  A  and 
surface  C  would  be 

r /»    V2 

=  Tac  =  (watts  per  cubic  inch)  — = —  deg.  C. 

Example;  when  the  frequency  is  60  cycles  and  the  flux  density 
is  75,000  lines  per  square  inch  then  the  watts  per  cubic  inch 
=  2.3  and 


106  ELECTRICAL  MACHINE  DESIGN 

=  0.8F2deg.C. 
.  C. 


The  fact  that  the  conductivity  along  the  laminations  is  so 
much  better  than  that  across  the  laminations  would  indicate  that 
axial  ventilation,  whereby  air  is  blown  across  the  ends  of  the 
laminations,  is  the  most  effective.  In  practice,  however,  nearly 
all  electrical  machines  are  cooled  by  means  of  radial  vent  ducts, 
and,  in  order  to  discuss  intelligently  the  effect  of  such  ducts,  it 
is  necessary  to  find  out  the  heat  resistance  between  the  surfaces 
B,  C  and  the  air. 

When  air  is  blown  across  the  surface  of  an  iron  core  at  V  ft. 
per  minute,  the  watts  dissipated  per  square  inch  of  radiating 
surface  for  1°  C.  rise  of  the  surface  temperature  is  found  by  ex- 
periment to  be  =  0.0245(1  +0.00127  7).1 

If  then,  as  in  case  (a),  all  the  heat  in  the  core  has  to  be  dis- 
sipated by  surface  B,  the  difference  in  temperature  between  sur- 
face B  and  the  air  =  Tb 

_  watts  per  square  inch  on  surface  B 

00245(1  +  0.00127  V) 
_  (watts  per  cubic  inch)  F 
0.0245(1  +  0.00127  7) 

Similarly  in  case  (b),  where  it  is  assumed  that  all  the  heat  is 
dissipated  by  surface  C,  the  difference  in  temperature  between 
surface  C  and  the  air  —  Te 

_  (watts  per  cubic  inch)  X 
0.0245(1  +  0.00127  7) 

Where  X=1.5  in.,  and  for  a  value  of  1  watt  per  cubic  inch,  the 
following  table  shows  the  values  of  Tab,  Tac,  Tb  and  Tc  for  dif- 
ferent values  of  Y  and  of  V. 

7  =  10,000 
Tb  Tc 

4.5          4.5 
9.0          4.5 
18.0          4.5 

These  results  are  plotted  in  Fig.  83  and  from  them  the  follow- 
ing general  conclusions  may  be  drawn:  — 

As  the  core  depth  Y  increases,  the  path  from  A  to  B  becomes 
long  compared  with  that  from  A  to  C  and,  therefore,  T0&  becomes 
comparable  with  Tac  in  spite  of  the  relatively  high  conductivity 
along  the  laminations. 

1  Ott,  Electrician,  March  7,  1907. 


7  = 

1000 

X 

F 

Tac 

Tab 

Tb 

Tc 

1.5 

1.5 

42 

0.75 

27 

27 

1.5 

3.0 

42 

3.0 

54 

27 

1.5 

6.0 

42 

12.0 

108 

27 

HEATING 


107 


The  area  C  increases  with  the  core  depth  while  area  B  remains 
constant  so  that  the  deeper  the  core  the  larger  the  part  of 
the  total  heat  which  is  conducted  across  the  laminations  and 
dissipated  from  the  surface  of  the  vent  ducts. 

92.  Limiting  Values  of  Flux  Density. 
The  peripheral  velocity  of  a  machine 

7tDa 

=  — Xr.p.m. 

_7iDa     pXr.p.m. 
p    X        12 


=  10XTX/  ft.  per  minute 


(16) 

therefore,  for  a  given  frequency,  the  peripheral  velocity  of  a 
machine  is  proportional  to  its  pole  pitch. 

For  a  given  axial  length  of  core,  the  longer  the  pole  pitch  the 
greater  the  flux  per  pole,  and  the  deeper  the  core  to  carry  this 
flux. 

Where  the  peripheral  velocity  of  a  machine  is  low,  the  core  is 
shallow,  the  vent  ducts  have  little  effect  on  account  of  their  small 
radiating  surface,  and  the  ventilation  is  poor;  the  loss,  however, 
is  small  because  there  is  not  much  iron  in  the  core. 

Where  the  peripheral  velocity  is  high  the  core  is  deep,  the  vent 
ducts  are  very  effective  on  account  of  their  large  radiating  surface, 
and  the  ventilation  is  good;  the  loss,  however,  is  large  since  much 
iron  is  used  in  the  core. 

For  a  given  frequency  the  same  flux  densities  can  be  used  for 
all  peripheral  velocities.  The  following  flux  densities  may  be 
used  for  D.  C.  machines  with  a  temperature  rise  of  40°  C.,  built 
with  iron  0.014  in.  thick,  the  relation  between  core  loss  and  flux 
density  being  as-  shown  in  Fig.  81 : 


Frequency 
(cycles  per  second) 

Flux  density  in  teeth 
(lines  per  square  inch) 

Flux  density  in  core 
(lines  per  square  inch) 

30 
40 
60 

150,000 
140,000 
125,000 

100,000 
85,000 
75,000 

Core  densities  higher  than  85,000  lines  per  square  inch  are 
seldom  used,  even  for  frequencies  that  are  lower  than  40  cycles, 
because  at  these  densities  the  core  becomes  saturated  and  the 


108 


ELECTRICAL  MACHINE  DESIGN 


cost  of  the  extra  field  copper  required  to  send  the  flux  through  a 
saturated  core  is  greater  than  the  cost  of  the  extra  iron  required 
to  keep  the  core  density  below  the  saturation  point.  There  is 
no  such  objection,  however,  to  high-tooth  densities  because  a 
machine  with  saturated  teeth  and  a  short  air  gap  is  just  as 
effective  in  preventing  field  distortion  as  a  machine  with  un- 
saturated  teeth  and  a  long  air  gap;  see  Art.  52,  page  61,  and 
does  not  require  any  more  excitation. 

93.  Heating  of  the  End  Connections  of  the  Winding. — The  end 
connection  heating  must  be  taken  up  separately  from  that  of  the 


II  II 

Length  of  End  Connections  in  Inches 

S  §  8  £  g 

/ 

v> 

/ 

/ 

/ 

<£> 

^ 

/ 

~jr 

^ 

^ 

-^ 

5          10          15          20          25        30 

Pole  Pitch  in  Inches 

FIG.  84. — Dimensions  of  coils. 

core  because  the  kind  of  radiating  surface  is  different  and  also 
the  manner  in  which  it  is  cooled. 

Since  the  resistance  of  copper  is  1  ohm  per  circular  mil  per 
inch  the  copper  loss  in  the  end  connections  of  one  conductor 

=  ^Tl<?  watts, 


and  the  total  copper  loss  in  the  end  connections 
M 


—  Z       /c2  watts. 


The  surface  by  which  this  loss  is  dissipated 

=  nDax2*c  sq.  in.     See  Fig.  84. 
^DaX^sq.in. 

since  Le,  as  shown  in  Fig.  84,  is  approximately  equal  to  1.6  X2^c 
for  standard  machines,  therefore  the  watts  per  square  inch 


HEATING 


109 


1.6 


M 


Amp.  cond.  per  in. 


Xa  constant. 


Circular  mils  per  ampere 

The  temperature  rise  of  the  end  connect  Jons  is  proportional  to 

the  watts  per  square  inch  of  radiating  surface,  it  is  therefore 

,•.,',  ...    amp.  cond.  per  in. 

proportional  to  the  ratio  -^— -  — n —  -  and  is  found  from  the 

,  cir.  mils  per  amp. 

curves  in  Fig.  85.  Two  curves  are  given,  one  for  machines  of 
large  diameter,  such  as  that  shown  in  Fig.  28,  and  the  other  for 
machines  of  small  diameter,  such  as  that  shown  in  Fig.  27.  For 
a  given  number  of  watts  per  square  inch  a  large  machine  runs 
cooler  than  does  a  small  one,  because  its  windings  are  not  so 
cramped  on  the  ends  and  the  free  passage  of  air  into  the  machine 
is  not  restricted  by  bearing  housings. 


FIG. 


1  2  3  4  5  6  x  10a 

Peripheral  Velocity  of  the  Armature  in  Ft.  per  Min. 

85. — Temperature  rise  of  armature  coils. 


94.  Temperature  Gradient  in  the  Copper  Conductors. — ab,  Fig. 
86,  is  a  conductor  which  is  carrying  current  and  which  is  embedded 
in,  and  insulated  from,  the  iron  core.  In  order  to  have  some 
idea  of  the  temperature  of  the  copper  in  the  center  of  the  core, 
consider  the  following  two  propositions. 

(a)  Assume  that  the  slot  insulation  is  much  thicker  than  that 
on  the  end  connections,  then  the  heat  in  the  embedded  portion  of 
the  winding  has  to  be  conducted  along  the  copper  and  dissipated 
at  the  end  connections.  It  is  required  to  find  the  difference  in 
temperature  between  c  and  a. 


110 


ELECTRICAL  MACHINE  DESIGN 


The  resistance  of  copper  is  1  ohm  per  circular  mil  per  inch  so 
that  the  energy  crossing  dx  =  Ic2  Rx 

_/2    X_ 

~Lc   M 

where  7C  is  the  current  in  the  conductor  in  the  slot; 
Rx  is  the  resistance  of  length  x  of  the  conductor; 
M  is  the  section  of  the  conductor  in  circular  mils; 
The  difference  in  temperature  between  two  faces  a  distance*  cte 


where  A  is  the  section  of  the  conductor  in  square  inches 

M 
"1.27X106 


FIG.  86. — Heat  paths  in  an  armature  conductor. 

11.1  is  the  thermal  conductivity  of  copper  in  watts  per  1  in. 
cube  per  1°  C.  difference  in  temperature. 

The  difference  in  temperature  between  the  center  c  and  any 

.X 

xdx        1 
point  X=(Vi»   |       ~YX1LI 


)   f 

J     C 


72cXl.27XlQ6     X2 
M2  <  2 

5.7X104XZ2 


(17) 


(cir.  mils  per  amp.)2' 

If,  for  example,  the  core  of  the  machine  is  20  in.  long,  so  that  the 
distance  from  the  center  of  the  core  to  the  end  is  10  in.,  and  the 
circular  mils  per  ampere  is  500,  then  the  difference  in  temperature 
between  the  copper  at  c  and  that  at  the  end  connections  =  23°  C. 

(b)  Consider  now  the  other  case  in  which  it  is  assumed  that 
the  end  connections  are  already  so  hot  that  the  heat  generated 
in  the  embedded  conductors  has  to  be  transmitted  through  the 
slot  insulation  and  dissipated  by  the  iron  core;  it  is  required  to 


HEATING  111 

find  the  difference  in  temperature  between  the  copper  and  the 
surrounding  iron. 

The  copper  loss  per  1  in.  axial  length  of  slot 
_  cond.  per  slotX/c2 

M 

_  amp.  cond.  per  slot 
cir.  mils  per  amp. 

If  this  heat  passes  through  the  insulation  then  the  difference  in 
temperature  between  the  inner  and  outer  layers  of  the  insulation 
_ /amp.  cond.  per  slot\      thickness  of  insulation         1 
=  \  cir.  mils  per  amp.  /  >  2d  +  s  *"O003' 

where  0.003  is  the  thermal  conductivity  of  ordinary  paper  and 
cloth  insulation  in  watts  per  inch  cube  per  1°  C.  difference  in 
temperature,  and  2d  +  s  is  the  area  of  the  path  per  1  in.  axial 
length  of  slot. 

Take  for  example  the  following  figures : 

Ampere  conductors  per  inch  =  760 

Slot  pitch  =0.88  in. 

Ampere  conductors  per  slot  =760X0.88  =  670 

Circular  mils  per  ampere       =  560 

d  =1.6  in. 

s  =0.43  in. 

Thickness  of  insulation          =0.07  in.,  including  clearance 

Temperature  difference  between  inner    and    outer    layers    of    insulation 

670     0.07         1 

560  A 3.63  A  0.003 
=  8  deg.  C. 

95.  Commutator  Heating. — The  modern  D.  C.  armature  is 
constructed  as  shown  in  Fig.  27;  the  commutator  is  smaller  in 
diameter  than  the  armature  core,  and  the  commutator  necks 
which  join  the  armature  winding  to  the  commutator  are  separated 
from  one  another  by  air  spaces,  so  that  when  the  armature  re- 
volves an  air  circulation  is  set  up  as  shown  by  the  arrows  in 
Fig.  87,  and  cool  air  is  drawn  over  the  commutator  surface. 

The  relation  between  permissible  watts  per  square  inch  of 
commutator  surface  and  commutator  peripheral  velocity,  ob- 
tained from  tests  on  non-interpole  machines,  is  shown  in 
Fig.  87. 

The  radiating  surface  is  taken  as  nDcF.  It  would  seem  that 
the  radiating  surface  ought  to  include  that  of  the  commutator 
necks.  It  is  found,  however,  that  a  considerable  portion  of  the 
commutator  neck,  such  as  from  a  to  b,  can  be  closed  up  without 


112 


ELECTRICAL  MACHINE  DESIGN 


affecting  the  commutator  ventilation  or  temperature  to  any 
great  extent;  just  how  much  of  the  surface  of  the  necks  should 
be  considered  as  radiating  surface  has  not  yet  been  determined 
experimentally. 

The  heat  to  be  dissipated  is  assumed  to  be  due  to  the  brush 
friction  and  contact  resistance  losses.  There  are  also  losses 
which  cannot  be  measured,  due  to  poor  commutation  and  to 
brush  chattering.  If  the  commutation  is  poor  and  the  brushes 


€ 


0,5  1.0  1.5          2.0          2.5          3.0         3.5  xlO3 

Peripheral  Velocity  of  the  Commutator  in  Ft.  per  Mm. 

FIG.  87. — Temperature  rise  of  commutators. 

chatter  badly  the  temperature  rise  may  be  higher  than  that 
obtained  by  the  use  of  the  curve  in  Fig.  87,  while  in  cases  where 
the  commutation  is  exceedingly  good  and  where  there  is  no 
chattering  the  temperature  rise  may  be  lower. 

96.  Application  of  Heating  Constants. — When  designing  a  new 
D.  C.  machine  for  a  guaranteed  temperature  rise  of  40°  C.  the 
core  heating  is  limited  by  keeping  the  flux  densities  below  the 
values  given  in  Art.  92,  page  107,  and  the  end  connection  heating 

amp.  cond.  per  in.   . 
is  limited  by  keeping  the  ratio    cir  mils  per  amp;  below  the 

values  given  in  Fig.  85,  page  109.  The  approximate  increase  in 
temperature  of  the  copper  at  the  center  of  the  core  over  the 
temperatures  of  the  iron  and  of  the  end  connections  is  found  by 


HEATING  113 

the  use  of  the  formulae  in  Art.  94.  The  design  is  then  compared 
with  designs  on  similar  machines  which  have  already  been  tested 
and  the  densities  modified  accordingly. 

The  results  of  careful  tests  on  similar  machines  should  always 
take  precedence  over  results  obtained  from  average  curves  and 
these  curves  should  always  be  changing  as  improvements  are 
made  in  the  methods  of  ventilation. 


CHAPTER  XII 

PROCEDURE  IN  ARMATURE  DESIGN 
97.  The  Output  Equation 

10-8  volts,     Formula  2,  page  11 


and 


paths     xDa 


10-' 
"60" 


and 


watts     60.8  X107 


nm 


The  value  of  Bg,  the  apparent  average  gap  density,  is 
limited  by  the  permissible  value  of  Bt,  the  maximum  tooth 
density,  which  value,  as  shown  in  Art.  92,  page  107,  is  about 


FIG.  88. — Effect  of  the  armature  diameter  on  the  tooth  taper. 

150,000  lines  per  square  inch  for  frequencies  up  to  30  cycles. 
That  Bg  also  depends  on  the  diameter  of  the  machine  may  be 
seen  from  Fig.  88;  the  smaller  the  diameter  the  greater  the  tooth 
taper  and  therefore  the  lower  the  gap  density  for  a  given  density 
at  the  bottom  of  the  teeth. 

114 


PROCEDURE  IN  ARMATURE  DESIGN 


115 


Fig.  89  shows  the  relation  between  Bg  and  Da  for  average 
machines;  in  cases  where  the  frequency  is  greater  than  30  cycles 
per  second  slightly  lower  values  of  Bg  must  be  used. 

The  value  of  q,  the  ampere  conductors  per  inch,  is  limited 
partly  by  heating  and  partly  by  commutation.  Suppose  that 

70  x  1C3 


20          40  60          80         100 

Armature  Diameter  in  Inches 


Ampere  Conductors  per  Inch 

,--- 

.  

.—  — 

J5, 

^ 

•** 

/ 

/ 

/ 

f 



.—  —  • 

^ 

-^ 

/ 

/ 

/ 

A      20          40          60          80         NX 
B    230        400         600         800       100 
Kilowatts 

Fio.F90. 

FIG.  89.                                                      FiG.^90. 

C        B       -Afi                                                      |_                                                     / 

to  ox  CT>  oo 
Watts  per  Sq.lnch  for  40°Cent.  "Rise 

3.0              x  10 
1.0 

1  2.0      0.8 

1 
S             0.6       0.3 

£ 
a  1.0      0.4       0.2 

a 
««i 

0.2       0.1 

^ 

mp.Cond.  per  Inch 

{ 

^  2.0 
9 
2  L6 

a  1.2 

S0.8 

a 

^ 

M 

0 

1 

Y\. 

/ 

. 

v° 

M 

? 

s 

/ 

•^ 

^ 

^ 

X 

C, 

/ 

s* 

/ 

/ 

/ 

< 

*v> 

/ 

f^T  ' 

/^ 

^ 

/ 

/ 

*^ 

^~ 

^*~ 

^\^ 

^' 

/, 

/ 

^ 

„  — 

x 

/ 

X 

no 

<v^ 

/, 

/ 

^ 

^ 

/ 

/ 

^ 

f 

/ 

/ 

// 

^ 

^ 

• 

/- 

^c 

^ 

^ 

A    20        40        60       80       100  ^ 
B   200      400      600     800      1000 
C  2000     4000     6000    8000    10000 
Watts 

1         2         3        4         5        6x10 
Peripheral  Velocity  in  Ft.  per  Min. 

FIG.  91. 


K.P.M. 


FIG.  92. 


FIGS.  89-92.  —  Curves  used  in  preliminary  design. 

for  a  given  rating  the  value  of  q  is  increased,  which  can  be  done 
by  increasing  the  number  of  conductors  in  the  machine  or  by 
decreasing  the  diameter.  If  the  number  of  conductors  be  in- 
creased the  reactance  voltage  will  be  increased,  as  ma}'  be  seen 


116  ELECTRICAL  MACHINE  DESIGN 

from  formula  12,  page  84.  If  the  diameter  is  decreased  the 
frame  must  be  made  longer  in  order  to  carry  the  flux  and  the 
slots  must  be  made  deeper  in  order  to  carry  the  larger  number 
of  ampere  conductors  on  each  inch  of  periphery,  both  of  which 
changes  increase  the  reactance  voltage.  In  order,  therefore,  to 
keep  the  reactance  voltage  within  reasonable  limits  it  is  neces- 
sary to  limit  the  value  of  q. 

It  is  found  that  q  depends  principally  on  the  kw.  output  of 
the  machine  and  the  relation  between  q  and  kw.  for  average 
machines  is  plotted  in  Fig.  90;  this  curve  may  be  used  for  pre- 
liminary design. 

98.  The  Relation  between  Da  and  Lc.  —  There  is  no  simple 
method  whereby  Da2Lc  can  be  separated  into  its  two  components 
in  such  a  way  as  to  give  the  best  machine,  the  only  satisfactory 
method  is  to  assume  different  sets  of  values  of  Da  and  LC)  work 
out  the  design  roughly  for  each  case,  and  choose  that  which 
will  give  good  operation  at  a  reasonable  cost. 

99.  Magnetic  and  Electric  Loading. 

volts 


60        paths 

rI1:10-8      watts 


and      ^atts=(^-)(^aXpoles),7T^f7r8.  (20) 

r.p.m.      Vpaths/ v  '60X108 

71 

The  term  -—rr-  is  called  the  electric  loading  and  is  the  total 
paths 

number  of  ampere  conductors  on  the  periphery  of  the  armature; 
the  larger  the  value  of  this  quantity  the  larger  the  amount  of 
active  copper  and  the  smaller  the  amount  of  active  iron  there  is 
in  the  armature. 

The  term  (<£«X  poles)  is  called  the  magnetic  loading  and  is  the 
total  flux  entering  the  armature;  the  larger  its  value  the  larger 
the  amount  of  active  iron  and  the  smaller  the  amount  of  active 
copper  there  is  in  the  machine. 

To  get  the  largest  possible  output  from  a  given  frame  both  the 
electric  loading  and  the  magnetic  loading  should  be  as  large  as 
possible. 

There  is  a  definite  ratio  between  the  magnetic  and  the  electric 
loading  which  will  give  the  cheapest  machine. 

.     magnetic  loading     <f>ap 
rheratl°  electric  loading  =ZTC 


PROCEDURE  IN  ARMATURE  DESIGN 


117 


ZIC 
=  B9</>LC 

2 

and  therefore  depends  largely  on  the  frame  length  Lc,  which 
quantity  is  limited  in  the  following  way: 

Figure  93  shows  one  field  and  one  armature  coil  for  a  D.  C. 
machine.  A  pole  of  circular  section  is  the  most  economical 
so  far  as  the  field  system  is  concerned  because  it  has  the  largest 
area  for  the  shortest  mean  turn  of  field  coil.  If  the  pole  be  rectan- 
gular in  section  then  that  with  a  square  section  has  the  largest 
area  for  the  shortest  mean  turn.  It  will  generally  be  found  that 

the  ratio  j-*-  -rr-  lies  between  the  values  1.1  and  1.7. 

frame  length 


FIG.  93. — Shape  of  field  and  armature  coils. 

The  pole  pitch  is  limited  by  armature  reaction;  thus  in  Art.  74, 
page  91,  it  was  shown  that  the  armature  ampere-turns  per  pole 
should  not  exceed  7500.  Further,  as  pointed  out  in  Art.  74,  the 

.    field  ampere-turns  per  pole  (gap  +  tooth)  . 
ratio  -  — i —    —  is  seldom  less  than 

armature  ampere-turns  per  pole 

1.2.  An  increase  in  the  armature  m.m.f.  per  pole,  therefore, 
requires  a  corresponding  increase  in  the  m.m.f.  of  the  main  field 
and  an  increase  in  the  radial  length  of  the  poles.  Rather  than 
allow  the  armature  ampere-turns  per  pole  to  exceed  7500,  it  will 
generally  be  found  economical  to  increase  the  number  of  poles, 
so  that  they  may  not  have  too  great  a  radial  length. 

For  7500  armature  ampere-turns  per  pole,  and  900  ampere 
conductors  per  inch,  the  pole  pitch  is  approximately 


118  ELECTRICAL  MACHINE  DESIGN 

^7500X2 

900 
-17  in. 

Lc  therefore,  as  pointed  out  above,  should  not  exceed  ^pr  =  15  in., 

except  in  the  special  case  where  the   peripheral  velocity  is  al- 
ready so  high  that  the  diameter  cannot  be  increased  and  the 
rating  can  only  be  obtained  by  the  use  of  an  extra  long  armature. 
If  Lc,  the  frame  length,  =15  in. 

Bg,  the  average  gap  density,  =60,000  lines  per  square  inch 
(/>,    the  pole  enclosure,  =0.7 

g,    the  ampere  conductors 

per  inch,  =900 

.    magnetic  loading 

then  A;,  the  ratio--,- ?-^-^ — T^- =700. 
electric  loading 

For  a  machine  with  a  small  armature  diameter  the  most 
economical  frame  length  will  be  less  than  15  in.;  for  example,  a 
machine  5  in.  in  diameter  and  15  in.  long  would  be  more  expen- 
sive and  would  give  more  trouble  than  one  which  had  the  same 
value  of  Da2LC)  but  a  diameter  of  9  in.  and  a  frame  length  of 
4.5  in.,  so  that,  since  k  depends  largely  on  the  length  Lc  its  value 
varies  with  the  diameter  of  the  machine.  Now 

watts  ..  •    i      v  1 

—  =  electric  loading X magnetic  loading X  AAN/in8 
r.p.m.  ou/\iu 

=  k  (electric  loading) 2  X  a  constant  (21) 

TTTQ  'j"i'Q 

and  for  each  value  of  -          -  there  is  a  value  of  k,  and  there- 
r.p.m. 

fore  of  electric  loading  (Z/c),  which  gives  the  most  economical 
machine.  Fig.  91  shows  the  relation  between  these  two  quanti- 
ties for  a  line  of  non-interpole  machines,  and  this  curve  may  be 
used  for  preliminary  design. 

It  must  be  understood,  and  will  be  seen  from  the  examples 
given  later,  that  the  value  of  k  may  vary  over  a  considerable 
range  without  affecting  the  cost  of  the  machine  to  any  consid- 
erable extent.  The  value  of  k  is  also  affected  by  the  cost  of  labor 
and  therefore  varies  under  different  conditions  of  manufacture. 

100.  Formulae  for  Armature  Design. 

A =  ^electricloading)2Xaconstant,formula21,  page  118. 

where  electric  loading  =  (Z/c) . 


PROCEDURE  IN  ARMATURE  DESIGN  119 

watts       60.8X107 
-Da*Lc=  x——  formula  19,  page  114. 


~E  =  Z<f>a  xs  X10-  formula  2,  page  11. 

-  Coils  =  k  |  +  1   for  a  series  winding  Art.  22,  page  22. 

Slots  =  k  oil  for  a  series  winding  Art.  22,  page  22. 


=  k         for  a  multiple  winding  with  equalizers 

Art.  22,  page  22. 

F   —  Slots  per  pole  should  be 

greater  than  12  for  small  machines 

greater  than  14  for  large  machines  Art.  71,  page  87. 

G  -Reactance  voltage  =  k  X  S  Xr.p.m.  X/CXLCX  T2X 


(formula  12,  page  84.) 

where  k  =  1.6    for  series  and  full-pitch  multiple  windings  ; 
=  0.93  for  short-pitch  multiple  windings. 

H  —  Reactance  voltage  =  0.7  (volts  per  pair  of  brushes)  when  the 

brushes  are  on  the  neutral  ; 
=  1.0  (volts  per  pair  of  brushes)  when  the 
brushes  are  shifted  from  the  neutral; 
Art.  73,  page  90. 

The  reactance  voltage  may  be  20  per  cent,  greater  than  this 
for  machines  with  series  windings  and  must  be  30  per  cent. 
less  for  those  with  short-pitch  multiple  windings. 

ZI 

J    —Armature  ampere-turns  per  pole  =  —  ^-  and  should  be 

less  than  7,500  Art.  74,  page  91. 

maximum  tooth  width  .  . 

K  --       —  ^—7  —  .,.,  —  =  1.1  for  large  machines; 

slot  width 

=  1.0  for  small  machines; 
these  are  approximate  values  found  from  practice 

L  —  Flux  density  is  taken  from  the  following  table 


120 


ELECTRICAL  MACHINE  DESIGN 


Cycles  per 
second 

Tooth-density 
lines  per  square  inch 

Core-density 
lines  per  square  inch 

30 
40 
60 

150,000 
140,000 
125,000 

100,000 
85,000 
75,000 

Art.  92,  page  107. 

M  —Commutator  dia.  =0.6  armature  dia.  for  large  machines; 

=  0.75  armature  dia.  for  small  machines. 
These  are  values  taken  from  practice.  Except  in  the  case  of 
turbo  generators  the  peripheral  velocity  of  the  commutator 
should  not,  if  possible,  exceed  3500  ft.  per  minute.  To  keep 
below  this  peripheral  velocity  it  may  be  necessary  to  use 
smaller  values  for  the  diameter  than  those  given  above. 

N  -  Wearing  depth  of  the  commutator,  namely,  the  amount 
that  can  be  turned  of  the  radius  without  making  the  com- 
mutator too  weak  mechanically  varies  from  0.5  in.  on  a  5-in. 
commutator  to  1.0  in.  on  a  50-in.  commutator. 


P   —  Brush  arc  should  be  less  than 


pole  pitch     comm.  dia. 


X    .          j  •" 


12         s  arm.  dia. 
and  should  not  cover  more  than   3  segments 

Art.  72,  page  89. 

Q    -Watts   per  square  inch  brush  contact  =  35  approximately 

Art.  64,  page  78. 

Vr 


R    —  Brush  friction  =1.25  A 


100 


watts 


formula  14,  page  98. 

10 1.  Preliminary  Design. — To  simplify  the  work  of  prelimi- 
nary design  the  necessary  formulae  and  curves  are  gathered 
together  above  and  the  method  of  procedure  is  as  follows: 

Find  the  electric  loading  ZIC  for  the  given  rating,  from  Fig.  91. 

71 

Find  g  =  -^  from  Fig.  90. 

7lUa 

From  these  two  quantities  find  Da  the  armature  diameter. 

Tabulate  three  preliminary  designs;  one  for  a  diameter  20  per 
cent,  larger  than  that  already  found  and  the  other  20  per  cent, 
smaller. 

Find  Bg,  the  apparent  gap  density,  from  Fig.  89. 


PROCEDURE  IN  ARMATURE  DESIGN  121 

Find  I/c,  the  frame  length,  from  formula  B,  page  119. 

Find  p,  the  number  of  poles,  which  should  have  such  a  value 

that  ~  ^TT;  lies  between  the  values  1.1  and  1.7.     Art.  99, 

frame  length 

page  117. 

Find  <t>a,  the  flux  per  pole,  =  Bg(/>rLc  where  ^  =  0.7  approx. 

Find  Z,  the  number  of  armature  face  conductors,  from  for- 
mula D. 

Choose  the  cheapest  winding  that  will  give  a  reactance  voltage 
below  the  desired  limit;  a  series  winding  is  generally  the  cheapest 
because  it  requires  the  smallest  number  of  coils  and  commutator 
segments. 

Find  S,  the  number  of  commutator  segments,  from  the  value 
of  Z  and  the  type  of  winding  used. 

Make  Dc,  the  commutator  diameter,  =  (0.6  to  0.75)  X  (armature 
diameter)  for  a  first  approximation. 

Find  the  brush  arc  from  formula  P. 

Find  the  commutator  length  so  that  the  watts  per  square  inch 
brush  contact  shall  not  exceed  35. 

Choose  between  the  different  designs. 

Example. — Determine  approximately  the  dimensions  of  a  D.-C.  generator 
of  the  following  rating: 

400  kw.,  240  volts,  1670  amperes,  200  r.p.m. 
The  work  is  carried  out  in  tabular  form  as  follows: 
Ampere  conductors 1.33X  108,  from  Fig.  91 


Ampere  conductors  per  ii 
Armature  diameter  
Apparent  gap  density  .  .  . 
Frame  length  
Poles  

nch.  .  . 
'.Bg 

..LC 

•  •  v 

.733,  froir 
.  .58  in. 
58,000 
12  in. 
10 

L  Fig.  90 
45  in. 
56,500 
20.5  in 

8 

70  in. 
59,000,  from  Fig.  89 
8  in.,  formula  B 
16,  formula  C 

Pole  pitch  . 

i 

18.2  in. 

17.6  ir 

L.        13.  8  in. 

Flux  per  pole  
Total  face  conductors  .  .  . 
Winding.  

.  .(f)a 

.Z 

8.8X106 
820 
,  .  one-turn 

14.  3X 
505 
multiple, 

106  4.55X106 
1590;  formula  D 
short-pitch 

Commutator  segments  .  .  , 
Reactance  voltage  

..S 
.  .RV. 

410 
1.5 

252 
2.0 

795 
1  .  2,  formula  G 

Commutator  diameter  .  .  . 
Brush  arc  .  . 

..DC 

35  in. 
.0.91  in. 

27  in. 
0.88  in 

42  in.,  formula  M 
0  .  69  in.,  formula  P 

Brush  length 

.10.5  in. 

13.5  in 

8.  5  in. 

Amperes  per  square  inch 
brush  contact 

of 

35 

35 

35 

Magnetic  loading  <f>ap 

640 

1090 

440 

Electric  loading       Zlc 

122  ELECTRICAL  MACHINE  DESIGN 

» 

The  second  machine,  which  has  an  armature  diameter  of  45 
in.,  has  the  largest  flux  per  pole  and  therefore  the  deepest  core  and 
the  heaviest  yoke.  It  is  the  longest  machine  and  therefore  the 
most  expensive  in  core  assembly.  It  has  the  smallest  number  of 
coils  and  commutator  segments  and  is  therefore  cheapest  in 
winding  and  commutator  assembly. 

The  third  machine,  which  has  an  armature  diameter  of  70  in., 
has  the  smallest  flux  per  pole  and  therefore  the  shallowest  core 
and  the  lightest  yoke.  It  is  the  shortest  machine  and  therefore 
the  cheapest  in  core  assembly.  It  has  the  largest  number  of  coils 
and  commutator  segments  and  is  therefore  the  most  expensive 
in  winding  and  commutator  assembly. 

The  first  machine  probably  costs  less  than  either  of  the  other 
two;  it  has  also  a  comparatively  low  reactance  voltage  and  should 
commutate  satisfactorily. 

Before  completing  the  design  with  the  58  in.  diameter  it  is 
advisable  to  design  the  machine  roughly  with  different  numbers 
of  poles  in  the  following  way: 

Poles 8  10  12 

Armature  diameter 58  in. 

Frame  length 12  in. 

Apparent  gap  density 58,000 

Pole  pitch 22.8  in.  18.2  in.  15.2  in. 

Flux  per  pole 11  .OX  106  8.8X  106  7.4X  106 

Total  face  conductors 658  820  975 

Winding one-turn  multiple,  short-pitch 

Reactan.ce  voltage 1.5  1.5  1.5 

Armature  ampere-turns  per  pole. 8550  6900  5700 

Commutator  diameter 35  in.  35  in.  35  in. 

Brush  arc 1.14  in.  0.91  in.  0.76  in. 

Brush  length 10 . 5  in.  10 . 5  in.  10 . 5  in. 

The  first  machine  is  most  expensive  in  material  due  to  the 
large  flux  per  pole  and  therefore  the  deep  core  and  the  large 
section  of  yoke. 

The  third  machine  is  most  expensive  in  labor  due  to  the 
number  of  coils  and  commutator  segments  that  are  required. 

The  reactance  voltage  is  the  same  in  each  case  but  the  armature 
ampere-turns  per  pole  is  greatest  in  the  first  machine  and  least  in 
the  last,  so  that,  so  far  as  commutation  is  concerned,  the  last 
machine  is  to  be  preferred,  and  the  first  one  should  not  be  used 
if  possible. 

Armature    Design. — Having    determined    the    approximate 


PROCEDURE  IN  ARMATURE  DESIGN  123 

dimensions  of  the  machine,  it  is  now  necessary  to  design  the 
armature  in  detail,  which  is  done  in  tabular  form  in  the  following 
way: 

Choose  the  10-pole  design  as  the  most  suitable,  then 

External  diameter  of  armature 58  in.  from  preliminary  design 

Frame  length 12  in.  from  preliminary  design 

Center  vent  ducts 3  —  0 . 5  in.  wide 

Gross  iron  in  frame  length 10. 5  in. 

Net  iron  in  frame  length 9 . 45  in. 

Poles 10 

Pole  pitch 18.2  in. 

Probable  flux  per  pole 8.8X  106  from  preliminary  design 

Probable  number  of  face  conductors ....  820  from  preliminary  design 

Winding.     The  minimum  number  of  slots  per  pole  =  14,  formula  F,  therefore 
the  minimum  number  of  total  slots   =140,  and  the  nearest  suitable 
number  is  200 
Conductors  per  slot         =  4 
Coils  =400 

Commutator  segments    =400 

Winding  =  one  turn  multiple,  short  pitch 

Reactance  voltage  =1.5,  formula  G 

167x800 
Ampere  conductors  per  inch  =  q  = -^—  =  730 

7C  /\  OO 

Amp.  cond.  per  inch 

-f~^ — -, —  —  =  1.3  for  40°  C.  rise,  from  Fig.  92 

Cir.  mils  per  amp. 

Circular  mils  per  ampere   560 

Amperes  per  conductor  at  full  load    167 
Section  of  conductor  =167X560   =93.500  circular  mils 

=  0.073  sq.  in. 

=0.91  in. 

0  91 
Probable  slot  width  =  ~—  =0.43  in.,  formula  K 

0.43    assumed  slot  width 

0 . 064  width  of  slot  insulation,  see  page  39 

0 . 04    clearance  between  coil  and  core 

0 . 326  available  width  for  copper  and  insulation  on  conductors. 

Use  strip  copper  in  the  slot  as  shown  in  Fig.  34  and  put  two  conductors 
in  the  width  of  the  slot;  make  the  strip  0.14  in.  wide  and  insulate  it  with 
half  lapped  cotton  tape  0.006  in.  thick. 

Depth    of    conductor  =  -^—T- =  0.52  in.;  increase  this  to  0.55  in.  to  allow 

for  rounding  of  the  corners. 
Slot  depth  is  found  as  follows : 


124  ELECTRICAL  MACHINE  DESIGN 

0 . 55    depth  of  each  conductor 

0 . 024  insulation  thickness  on  each  conductor 

0.084  depth  of  slot  insulation,  see  page  39. 


0 . 658  depth  of  each  insulated  coil 

2  number  of  coils  in  depth  of  slot 

1.316  depth  of  coil  space 

0 . 2      thickness  of  stick  in  top  of  slot 


1.516  necessary  depth  of  slot;  make  it  1.6  in.  deep. 
Diameter  at  bottom  of  slot  .....  .  ......  54.8  in. 

Slot  pitch  at  bottom  of  slot  ...........  0.86  in. 

Minimum  tooth  width  ................  .  0.43  in. 

900 
Tooth  area  per  pole  =  —  X  0.7X0.43X9.45  =  57  sq.  in. 

Flux  per  pole  with  800  conductors  ........  9X  106  for  240  volts,  formula  D- 

Maximum  tooth  density  ...................  158,000  lines  per  square  inch. 

this  density  is  not  too  high  so  that  the  core  does  not  need  to  be  length- 

ened. 
Flux  density  in  the  core,  assumed  ............  85,000  lines  per  square  inch 

9X  106 
Core  area  - 


2X8OO  ..............  '- 

„.        ,     ,,      core  area 

Core  depth  =  —  —  :  ---  ................  5.6  in. 

net  iron 

Internal  diameter  of  armature  ..........  43.6  in. 

The  above  data  is  now  filled  in  on  the  armature  design  sheet  shown  on 
page  125. 

Commutator  Design. 

Commutator  diameter,  assumed  to  be  0.6  (armature  diameter)  =35  in. 
Number  of  commutator  segments  ......  400 

Width  of  one  segment  and  mica71          =  0.275  in. 

400 

Brush  arc  ...........................  0.91  in.,  formula  P. 

Use  a  brush  0.75  in.  thick  set  at  an  angle  of  30°,  so  that  the  brush  arc 

=  0.87  in. 
Segments  covered  by  brush  ...........  .3.1 

Amperes  per  set  of  brushes  =  —  —  X  2  =  334 

poles 

Amperes  per  square  inch  of  brush  contact,  35  assumed 
Necessary  brush  length  ................  11  in. 

Brushes  per  stud,  use  6  brushes,  each  0.75  in.  X  1.75  in. 
Commutator  length  =  6(1.  75  +  0.25)  +  1  =  13  in. 

allow  0.25  in.  between  brushes  and  1  in.  additional  clearance 
Peripheral  velocity  of  commutator  ......  1830  ft.  per  minute. 

Total  brush  contact  area  =  10X6X  1.75X0.87  =  91  sq.  in. 
Commutator  friction  loss  ..............  2100  formula  R. 

Volts  drop  per  pair  of  brushes  ..........  2.5     formula  H. 


PROCEDURE  IN  ARMATURE  DESIGN 


125 


Contact  resistance  loss  =  2. 5  X  1670  =  4200  watts 
Watts  per  square  inch  of  commutator  surface  = 


4200  +  2100 


7TX35X13 
=  4.4 

Probable  temperature  rise  on  commutator        =40°  C.,  from  Fig.  92. 

Had  the  commutator  temperature  rise  come  out  too  high,  it  would  have 
been  necessary  to  have  used  brushes  with  lower  contact  resistance,  which 
might  cause  the  commutation  to  be  poor,  or  else  to  have  increased  the  com- 
mutator radiating  surface. 

The  above  data  is  now  filled  in  on  the  design  sheet  shown  below. 

102.    Armature  and  Commutator  Design  Sheet. 


Armature 

External  diameter 58  in. 

Internal  diameter ^3.5  in. 

Frame  length 12  in. 

End  ducts 2-1/2  in. 

Center  ducts 3-1/2  in. 

Gross  iron 10.5  in. 

Net  iron 9.45  in. 

Slots,  number 200. 

size 0.43  in.  XI. 6  in. 

Cond.  per  slot,  number 4. 

size. .  .0.14  in. X  0.55  in. 

Coils 400. 

Turns  per  coil 1. 

Total  conductors 800. 

Winding,  type multiple. 

pitch 1-20. 

Slot  pitch 0.91  in. -0.86  in. 

Tooth  width 0.48  in. -0.43  in. 

Max.  tooth  width 


....1.11. 

.5.65  in. 
..18.2  in. 

0.7. 

57  sq.  in. 


Slot  width 

Core  depth 

Pole  pitch 

Per  cent,  enclosure  .... 
Min.  tooth  area  per  pole 
Core  area  per  pole 53  sq.  in. 

Apparent  gap  area  per  pole  153  sq. 
in. 

Densities,  Iron  loss,  Excitation 
Flux  per  pole,  no-load 9X  106. 

Maximum  tooth  density  (apparent), 
158,000  lines  per  square  inch. 

Maximum  tooth  density  (actual), 
150,000  lines  per  square  inch. 

Core  density,  85,000  lines  per  square 
inch. 


35  in. 

13  in. 

400. 

0.275  in. 

0.03  in. 

1  in. 

0.87  in. 

10. 

"  X  If")- 


Commutator 

Diameter 

Face 

Bars 

Bar  and  mica 

Mica 

Wearing  depth 

Brush  arc 

Brush  studs 

Brushes  per  stud 6  (f 

Amperes  per  square  inch  contact .  37. 
Peripheral  velocity  ft.  per  min.,  1830. 

Friction  loss,  watts, 2100 

Volts  per  pair  of  brushes, 2.5. 

Contact  resistance  loss,  watts,. 4200. 
Watts  per 'square  inch  surf  ace.  .4.4. 

Temperature  rise,  deg.  C 40. 

Average  volts  per  bar 6. 

Cross-connect  every  fourth  coil. 
Size   of   cross-connectors;   half  the 

conductor  section. 

Copper  loss,  Commutation 

Amp.  cond.  per  inch 730. 

Circular  mils  per  ampere 560. 

Length  of  conductor 42  in. 

Copper  loss 10  kw. 

Volts    drop    in    armature  =-p-  =  6 

(formula  15,  page  103). 

Armature  AT.  per  pole 6700. 

^         AT  (gap  +  tooth) 

J-tcitlO  A    m  *~~ 

arm.  AT.  per  pole 


1 . 24. 


Reactance  voltage 1.5. 


126 


ELCTRICAL  MACHINE  DESIGN 


Gap  density  (apparent),  59,000  lines 

per  square  inch. 

Weight  teeth 385  Ib. 

core 2300  Ib. 

Frequency,  eye.  per  second,  ....  16.6. 
Iron  loss,  6450  watts  (Art.  84,  page 

102). 
Air  gap  clearance 0.3  in. 

Carter  coefficient 1.12. 

AT.  gap,  Art.  46 6200. 

AT.  tooth,  Art.  46 2080. 


Rating 

Kilowatt 400. 

Volts  no-load 240. 

Volts  full-load 240. 

Amperes 1670. 

R.  p.  m 200. 

Magnetic  loading 
Electric  loading 

Output  f  actor  =  =  5' 


CHAPTER  XIII 
MOTOR  DESIGN  AND  RATINGS 

103.  Procedure  in  Design. — The  design  of  a  D.-C.  motor  is 
carried  out  in  exactly  the  same  way  as  that  of  a  D.-C.  generator. 

Example. — Determine  approximately  the  dimensions  of  a  D.-C.  shunt 
motor  of  the  following  rating: 

30  h.p.,  120  volts,  900  r.p.m. 

Probable  efficiency  .  =90  per  cent. 

Full- load  current  =208  amperes. 

Kilowatt  input  =25. 

Ampere  conductors  =0.19X105,  from  Fig.  91. 

Ampere  conductors  per  inch  =480,  from  Fig.  90. 

Armature  diameter  =  12.5  in. 

Apparent  gap  density,  Bg  =44,000,  from  Fig.  89. 

Frame  length,  Lc  =7.3,  from  formula  B,  page  119. 

Poles  =4,  from  formula  C. 

Pole  pitch  =9.8  in. 

Flux  per  pole  =2.2X  106  =  5^LC. 

Total  face  conductors  =364  for  multiple  winding. 

=  182  for  series  winding,  formula  D. 
Reactance  voltage  =1.0  for  a  full- pitch  multiple  winding  with  one  turn  per 

coil, 

=  2 . 0  for  the  same  winding  with  two  turns  per  coil, 
=  2.0  for  a  series  winding  with  one  turn  per  coil, 

formula  G. 

Winding:  The  series  winding  is  the  cheapest  since  it  requires  half  as  many 
coils  and  commutator  bars  as  are  required  for  the  one-turn  multiple 
winding,  and  it  does  not  require  equalizers  as  in  the  case  of  the 
two-turn  multiple  winding. 

Commutator  diameter  =  0. 75 X  Armature  diameter  =9.5  in.,  formula  M. 
Brush  arc  =0.61  in. 

Brush  length  =5.0  in. 

Amperes  per  square  inch  of  brush  contact  =35. 

While  working  on  the  preliminary  design  it  is  desirable  to 
find  the  probable  pole  area  and  see  if  a  circular  section  is  suit- 
able for  the  particular  diameter  and  frame  length  that  have 
been  chosen. 

Flux  in  pole  =<£aX leakage  factor. 

=  2.2X  106X  1.25  approximately. 

=  2.75X106  approximately. 

Pole  area,  assuming  a  pole  density  of  95,000  lines  per  square  inch 

127 


128  ELECTRICAL  MACHINE  DESIGN 

_2.75X106 
95000 

=  29  sq.  in. 
Pole  diameter  for  a  circular  section  =  6  in.  which  is  suitable  for  a  frame 

length  of  7.3  in. 
Armature  Design. 

External  diameter  =12.5  in.  from  preliminary  design. 

Frame  length  =7.3  in.  from  preliminary  design. 

Center  vent  ducts  =  2  -  0.375  in.  wide,  Art  23,  page  24. 

Gross  iron  in  frame  length  =6.55  in. 

Net  iron  in  frame  length  =5.9  in. 

Probable  number  of  face  cond.  =182  from  preliminary  design. 

Winding:     The  minimum  number  of  slots  per  pole  =  12,  formula  F,  page 
119,  therefore: 

The  minimum  number  of  total  slots  =48. 

The  number  of  slots  should  =  k  —  ±1  for  a  series  winding,  see  Art.  22, 

page  22,  and  the  nearest  suitable  number  of  slots  =  49. 

Conductors  per  slot  =  4. 

Coils  =98  with  one  dead,  see  Art.  22,  page  22. 

Commutator  segments  =97. 

Winding  =  one- turn  series. 

Reactance  voltage  =2.1. 

Active  conductors  =194. 

The  remainder  of  this  design  is  worked  out  in  exactly  the  same 
way  as  that  for  the  generator  in  Art.  101 ,  page  120,  and  the  final 
result  is  tabulated  below. 

104.  Armature  and  Commutator  Design  Sheet. 

Armature  Commutator 

External  diameter 12.5  in.  Diameter 9.5  in. 

Internal  diameter 6.0  in.  Face 6.75  in. 

Frame  length 7.0  in.  Bars 97. 

End  ducts none.  Bar  and  mica 0.308  in. 

Center  ducts 2-3/8  in.  Mica 0.03  in. 

Gross  iron 6.25  in.  Wearing  depth 0.5  in. 

Net  iron 5.6  in.  Brush  arc 0.58  in. 

Slots,  number  . .  . 49  Brush  studs  4. 

size 0.4  in.  X  0.92  in.  Brushes  per  stud.  .3(1/2  in.Xl  3/4 

Conductor  per  slot,  number 4.  in.). 

size 0.12  in.  X  0.32  in.  Amperes  per  square  inch  contact,  35. 

Coils 98  (1  dead).  Peripheral  velocity  ft.  per  min.  2240. 

Turns  per  coil 1.  Friction  loss,  watts 340. 

Total  conductors 194.  Volts  per  pair  of  brushes 2.0. 

Winding,  series;  pitch 1-13.  Contact  resistance  loss,  watts  .416. 

Slot  pitch 0.8  in.  and  0.685  in.  Watts  per  square  inch  surface  .  3.75. 

Tooth  width 0.4  in.  and  0.285  in.  Temperature  rise 35°  C. 


MOTOR  DESIGN  AND  RATINGS 


129 


Armature 
Maximum  tooth  width 


Commutator 


1.0. 


Average  volts  per  bar 5.0. 

Cross  connect none. 

Size  of  cross-connectors none. 

Coppsr  loss,  Commutation 
Amperes  conductors  per  inch  .  .  515. 

Circular  mils  per  ampere 470. 

Length  of  conductor 25  in. 


Volts  drop  in  armature  .  .  . 
Armature  AT.  per  pole  .  .  . 

Ratio  AT(gap+t°°th) 

5.1. 

.  .  .  2600. 

# 

1  3^ 

arm.  AT.  per  pole 
Reactance  voltage  . 

...2.05. 

Rating 

H.P 30. 

Volts 120. 

Amperes 208. 

R.p.m 900. 

Magnetic  loading 


Electric  loading 
Output  factor .... 


.400. 
.  ;2.5. 


Slot  width 

Core  depth 2.33  in. 

Pole  pitch 9.8  in. 

Per  cent,  enclosure 0.7. 

Min.  tooth  area  per  pole.  .  .  13.7  sq.  in. 

Core  area 13  sq.  in. 

Apparent  gap  area  per  pole .  .  48  sq.  in. 

Densities,  Iron  loss,  Excitation 

Flux  per  pole 2.07X106. 

Maximum  tooth  density   (apparent), 

150,000  lines  per  square  inch. 
Maximum    tooth     density     (actual), 

142,000  lines  per  square  inch. 
Core  density,  80,000  lines  per  square 

inch. 
Apparent  gap  density,  43,000  lines  per 

square  inch. 
Weight,  teeth 24  Ib. 

core 96  Ib. 

Frequency 30  cycles. 

Iron  loss 630  watts. 

Air  gap  clearance 3/16  in. 

Carter  coefficient 1.2. 

AT.  gap 3000. 

A.T.  tooth 500. 

105.  Motor   Ratings  for  Different  Voltages  and  Speeds. — An 
open  type  shunt  motor  rated  at  30  h.  p.,  120  volts,  208  amperes, 
900  r.p.m.  is  built  as  follows: 
Armature 

External  diameter  .  . 12.5  in. 

Frame  length 7.0  in. 

Slots,  number 49. 

size 0.4  in.  X0.92  in. 

Conductors  per  slot,  number 4 

size 0.12  in.  X  0.32  in. 

Coils 98,  1  dead. 

Winding,  one-turn  series (I.T.S.). 

Commutator 

Diameter ' 9.5  in. 

Face 6.75  in. 

Bars,  number 97. 

It  is  required  to  design  armatures  for  the  following  open  shunt 
ratings : 


130 


ELECTRICAL  MACHINE  DESIGN 


500  volts,    950  r.p.m. 

220  volts,  1200  r.p.m. 

220  volts,    600  r.p.m. 

Find  the  Windings. — In  order  to  use  the  same  poles,  yoke  and 
armature  parts,  it  is  necessary  that  the  flux  per  pole  be  the 
same  in  each  case. 


60 


=  a  constant 


paths 
/ZXr.p.m.x 
\    paths     / 


paths 

By*the  use  of  the  above  formula  the  work  is  carried  out  in  tabular 
form  as  follows: 


E 

R.P.M. 

Winding 

Paths 

Total 
Conductors 

Slots 

Conduc- 
tors 
per  slot 

Commu- 
tator 
segments 

A 
B 

c 

120 
500 

220 

900 
950 

1200 

1  T.  S.  (1  dead) 
1  T.  S.  (1  dead) 
2  T.  S.  (1  dead) 
ITS 

2 
2 
2 
2 

194  active 
782  active 
780  active 
265  active 

49 
49 
49 
53 

4 
16 
16 
5 

97 
391 
195 
cannot  wind 

1  T.  M  

4 

530  active 

53 

10 

265 

D 

220 

600 

1  T.  S  

2 

530  active 

53 

10 

265 

In  design  B,  the  number  of  commutator  segments  with  a  one- 
turn  series  winding  is  391  and  the  thickness  of  one  copper  and  one 
mica  segment  taken  together  =0.077  in.  for  a  commutator  9.5 
in.  diameter.  This  value  is  rather  small  and  a  commutator  with 
such  a  large  number  of  thin  segments  is  liable  to  develop  high 
bars. 

With  a  two-turn  series  winding,  half  the  number  of  segments 
are  required,  but  the  reactance  voltage  is  twice  as  large  so 
that  the  machine  will  probably  require  high  resistance  brushes; 
this  will  have  to  be  decided  after  the  current  rating  has  been 
found  and  the  reactance  voltage  determined. 

In  design  C,  265  conductors  are  required  with  a  one-turn  series 
winding,  so  that  49  slots  cannot  be  used  and  a  new  armature 
punching  must  be  designed.  The  minimum  number  of  slots  per 
pole  is  12  and  of  total  slots  is  therefore  48.  A  winding  with  65 
slots  and  four  conductors  per  slot  might  be  used  but  in  that  case 
the  slot  would  be  very  narrow  and  the  tooth  very  weak.  A 
one-turn  series  winding  with  53  slots  and  five  conductors  per 


MOTOR  DESIGN  AND  RATINGS 


131 


slot  cannot  be  used  since  the  number  of  conductors  per  slot 
must  be  a  multiple  of  2  for  a  double  layer  winding;  it  is  possible, 
however,  to  use  53  slots  with  a  one-turn  multiple  winding  and  10 
conductors  per  slot. 

Find  the  Size  of  Slot. — In  order  that  the  tooth  density  be  the 
same  in  each  case  it  is  necessary  that  the  slot  area  per. pole  be 
unchanged.  The  original  machine  had  49  slots,  0.4  in.  wide; 
when  53  slots  are  used  they  must  be  made  narrower  and 

=  0.4X49 
53 

=  0.37  in.  wide. 

The  depth  of  slot  is  kept  the  same  and  therefore  the  core  density 
is  unchanged. 

Find  the  Size  of  Conductor. — In  order  to  get  the  largest  pos- 
sible rating  out  of  the  machine  the  size  of  conductor  should  be 
the  largest  that  can  be  got  into  the  slot  without  making  the  coil 
too  tight  a  fit. 
,    The  size  of  conductor  is  given  in  the  following  table: 


Slot  size 

Conductors  per  slot 

Size  of  conductor 

0.4   X0.92 

4 

0.  12  in.  X  0.32  in. 

0.4   X0.92 

16 

No.  11  B.  &  S. 

0.37X0.92 

10 

No.    9  B.  &  S. 

0.37X0.92 

10 

No.    9  B.  &  S. 

Find  the  Ampere  Rating. — The  current  in  each  conductor  should 

,.    amp.  cond.per  in. 

be  such  that  the  ratio  -^—^ — ^ —  -  shall  not  exceed  the 

cir.  mils  per  amp. 

value  found  from  Fig.  92,  page  115,  and  the  work  is  carried  out  in 
tabular  form  as  follows: 


R.P.M. 

Peri  p.  velocity 

amp.  cond.  per  in. 

Total 
conductors 

Size  of 
conductors 

cir.  mils  per  amp. 

900 

2950  ft.  per  min. 

1.07  from  Fig.  92 

194 

0.12//X0.32// 

950 

3100  ft.  per  min. 

1.12  from  Fig.  92 

780 

No.  11  B.  &S. 

1.200 

3920  ft.  per  min. 

1.32  from  Fig.  92 

530 

No.    9B.  &S. 

600 

1960  ft.  per  min. 

0.83  from  Fig.  92 

530 

No.    9B.  &S. 

132 


ELECTRICAL  MACHINE  DESIGN 


,         Amperes  per 
conductor 

Ampere  conductors 
per  inch 

Circular  mils  per 
ampere 

104 

515 

470 

21.5 

430 

380 

36 

490 

365 

28 

380 

470 

The  horse-power  of  the  machine  is  found  as  follows: 


Volts 

Amperes 

Assumed 
efficiency 

Horse-power 

Reactance 
voltage 

120 

208 

0.89 

30 

2.05 

500 

43 

0.89 

25 

3.6 

220 

144 

0.89 

37.5 

1.3 

220 

56 

0.87 

14 

1.0 

Discussion  of  Ratings. — If  the  flux  be  constant  the  volts  per 
conductor  is  directly  proportional  to  the  speed. 

The  total  volume  of  current  in  the  armature  =  the  total  cross- 
section  of  copper  in  the  armature  X  the  current  density  in  that 
section. 

The  total  input  into  the  machine  =  volts  per  conductor  X 
total  current  volume,  and  so  is  proportional  to  r.p.m.  X  total 
section  of  copper  X  current  density,-  so  that  in  the  case  of 
high  voltage  motors,  where  the  total  number  of  conductors  is 
large  and,  therefore,  the  space  factor  of  the  slot — namely,  the 

section  of  copper  in  the  slot  .  „      ,  .          .     , 

— T—      .   ,    T  ,      — —     -  is   small— the   value    of    the    total 
the  total  slot  section 

section  of  copper  is  lower  than  in  the  case  of  a  low  voltage  motor 
built  on  the  same  frame,  and  therefore  the  rating  has  to  be  lower. 

In  the  case  of  very  slow  speed  motors  the  number  of  conductors 
is  generally  large  so  as  to  get  the  desired  voltage  and  the  current 
density  is  low  because  of  the  poor  ventilation;  for  these  reasons 
motors  have  to  be  rated  down  more  than  in  proportion  to  the 
speed. 

106.  Calculation  of  Efficiency. — It  is  required  to  calculate  the 


MOTOR  DESIGN  AND  RATINGS  133  * 

efficiency  of  the  machine  whose  design  data  is  given  on  page  128. 
Before  this  can  be  determined  it  is  necessary  to  find  the  bearing 
friction  and  also  the  excitation  loss. 

The  bearings  measure  2.5  in.  X6.25  in. 
The  rubbing  velocity  at  900  r.p.m.  =590  ft.  per  minute. 
Thefrictionloss=2X0.8lX2.5x6.25X(5.9)3'2,   formula  13,  page  97. 
=  360  watts. 

The  probable  excitation  loss  may  be  found  as  follows: 

Ampere-turns  (gap  +  tooth)  =  3000  +  500  =3500,  from  design  sheet. 
The  probable  field  excitation  =  3500  X  1.25  =  4400  ampere- turns. 


mi_    i       XT.  T       amp. -turns  mean  turn 

The  length  L/  =  - 


F ext.  periphery  X  watts  per  sq.  in.  X  d/  X  s/X  1 .27 

(Formula  8,  page  66)  where 

j    pole  diameter  =6  in.  from  preliminary  design 

df  =2  in.,  assumed 

mean  turn  =25  in. 

external  periphery  =31  in. 

watts  per  square  inch  =0.8,  from  Fig.  56 

space  factor  =0.65,  approximately,  from  Fig.  57 

therefore  L/  for  4400  ampere- turns      =3.5    in. 
The  excitation  loss  =  external  surface  of  coil  X  watts  per  square  inch  X 

number  of  coils 
=  31X3.5X0.8X4 
=  350  watts. 

The  total  losses  therefore  are 
Bearing  friction  =360  watts. 

Excitation  loss  =350  watts. 

Iron  loss  =630  watts,  from  design  sheet. 

Armature  copper  loss  =1,070  watts,  from  design  sheet. 

Commutator  friction  loss      =340  watts,  from  design  sheet. 
Commutator  resistance  loss  =416  watts,  from  design  sheet. 

Total  loss,  3166    watts. 

Output-  (=30h.p.)  =22,400  watts. 

Input  =25,566  watts. 

Efficiency  =88  per  cent. 

107.  Rating  as  an  Enclosed  Motor. — Experiment,  shows  that 
in  the  case  of  a  totally  enclosed  motor  the  temperature  rise  of  the 
coils  and  core  of  the  machine  is  proportional  to  the  total  loss 
(neglecting  bearing  friction  which  seems  to  be  conducted  along 
the  shaft  and  dissipated  by  the  pulley)  and  is  independent  of  the 
distribution  of  this  loss.  The  temperature  rise  is  also  found  to 
vary  inversely  as  the  external  radiating  surface  and  to  depend 


134 


ELECTRICAL  MACHINE  DESIGN 


on  the  peripheral  velocity  of  the  armature  in  the  way  shown  in 
Fig.  94. 

In  the  machine  which  has  already  been  discussed  in  this 
chapter  the  external  diameter  of  the  yoke  =  28  in. 
The  length  of  the  frame  axially  =  24  in.  approx. 

The  external  surface  =3340  sq.  in.;   Fig.  94 

The  total  loss  neglecting  bearing  friction   =  2800  ^watts  at  a  load 
of  30  h.p.;  Art.  106. 

Watts  per  square  inch  =0.85 

Probable  temperature  rise  =80°  C. 


$ 

5 

-g    0.014 

g 

M    0.012 

c8 
§ 

=2    0.010 

s 

02 

|   0.008 

K    0.006 
o 

g   0.004 

M 
1 

|  0.002 

te 

^ 

^^ 

•" 

\ 

X 

s 

^^ 

j 

/     - 

> 

• 

.\ 

^ 

Bai 

iating 

Surfac 

)  ™  T^) 

(?« 

^ 

0  I  2  3  4xl03 

Armature  Peripheral  Velocity  in.  Ft.  per  Min. 

FIG.  94. — Heating  curve  for  enclosed  motors. 

In  order  to  lower  the  temperature  rise  it  is  necessary  to  lower 
the  rating  so  as  to  cut  down  the  losses.  The  horse-power  is 
reduced  so  as  to  cut  down  the  current,  and  the  speed  is  increased 
so  as  to  cut  down  the  flux  and,  therefore,  the  core  loss  and  the 
excitation  loss. 

In  the  machine  under  discussion  let  the  horse-power  be  reduced 
30  per  cent,  and  the  speed  be  increased  20  per  cent.,  the  losses 
will  then  be  changed  as  follows: 

Excitation  loss  is  proportional  to  the  ampere-turns  and  this 
will  be  reduced  about  20  per  cent.,  due  to  the  decrease  in  flux. 

Iron  loss  is  found  by  the  use  of  the  curves  in  Fig.  81  for  20  per 
cent,  lower  densities  and  20  per  cent,  higher  frequency. 

Armature  copper  loss  is  proportional  to  the  (current)2  and  is 


MOTOR  DESIGN  AND  RATINGS  135 

therefore  reduced  to  ^-^of  its  original   value,   due  to  the  de- 
crease in  horse-power. 

Brush  friction  loss  will  be  reduced  30  per  cent,  because  less 
brush  area  is  required  and  will  be  increased  20  per  cent,  because 
of  the  increase  in  speed. 

Contact  resistance  loss  will  be  proportional  to  the  current  since 
the  current  density  in  the  brush  is  kept  constant  and  the  volts 
drop  per  pair  of  brushes  is  unchanged. 
The  losses  then  will  be  as  follows: 

30  h.p.  900  r.p.m.  23  h.p.  1080  r.p.m". 

Excitation  loss  350  290 

Iron  loss  630  580 

Armature  copper  loss  1070  630 

Commutator  friction  loss  340  315 

Contact  resistance  loss  416  320 


Total  loss,  2806  2135 

Watts  per  square  inch  for  1°  C.  rise  =0.0105  0.0118,  from  Fig.  94. 

Square  inch  radiating  surface  3340  3340 

Watts  per  square  inch  0 . 84  0 . 64 

Probable  temperature  rise  80°  C.  55°  C. 

108.  Possible  Ratings  for  a  given  Armature. — The  following 
ratings  are  generally  recognized  by  manufacturers  of  small 
motors  and  are  given  to  show  approximately  what  a  motor  can 
do  under  different  conditions  of  operation. 

Continuous  Duty,  Constant  Speed,  Open  Shunt  Motors. — For 
such  machines  the  usual  temperature  guarantee  is  that— the 
temperature  rise  shall  not  exceed  40°  C.  by  thermometer  after  a 
continuous  full-load  run,  nor  shall  it  exceed  55°  C.  after  2 
hours  at  25  per  cent,  overload  immediately  following  the  full- 
load  run. 

The  guarantee  for  commutation  is  that  the  machine  shall 
operate  over  the  whole  range  from  no-load  to  25  per  cent,  over- 
load without  destructive  sparking  and  without  shifting  of  the 
brushes. 

Continuous  Duty,  Constant  Speed,  Screen-covered  Shunt 
Motors. — Due  to  the  resistance  of  the  perforated  sheet  metal 
that  is  used  to  close  up  all  the  openings  in  the  machine  to  the 
free  circulation  of  air,  the  temperature  rise  will  be  about  20 
per  cent,  higher  than  that  for  the  same  machine  operating  as  an 
open  motor. 


136  ELECTRICAL  MACHINE  DESIGN 

Continuous  Duty,  Constant  Speed,  Enclosed  Shunt  Motors. — 

For  such  machines  the  temperature  guarantee  is  that — the  tem- 
perature rise  inside  of  the  machine  shall  not  exceed  65°  C.  by 
thermometer  after  a  continuous  full-load  run.  An  overload  tem- 
perature guarantee  is  seldom  made. 

To  keep  within  this  guarantee  the  standard  open  motor  is 
generally  given  a  30  per  cent,  lower  horse-power  rating  so  as  to 
reduce  the  armature  current,  and  is  run  at  20  per  cent,  higher 
speed  so  as  to  reduce  the  flux  per  pole  and  therefore  the  iron  loss 
and  the  excitation  loss. 

Elevator  Rating,  Open  Compound  Motor. — For  such  service 
the  usual  temperature  guarantee  is  that — the  temperature  rise 
shall  not  exceed  45°  C.  after  a  full-load  run  for  1  hour  and  that, 
immediately  after  the  full-load  run,  the  machine  shall  carry  50 
per  cent,  overload  for  1  minute  without  injury. 

To  obtain  this  rating  the  standard  open  motor  is  rated  up 
about  20  per  cent.  The  compound  field  is  generally  made 
about  30  per  cent,  of  the  total  field  excitation  at  full-load  so 
that  the  starting  current  will  be  less  than  it  would  be  with  a 
shunt  motor  of  the  same  rating.  For  elevator  service  the  brushes 
must  be  on  the  neutral  position  so  that  the  motor  can  operate 
equally  well  in  both  directions. 

Crane  Rating,  Totally  Enclosed  Series  Motor. — For  such  serv- 
ice the  usual  temperature  guarantee  is  that — the  temperature 
rise  inside  of  the  machine  shall  not  exceed  55°  C.  after  a  full- 
load  run  for  half  an  hour,  the  machine  shall  also  carry  50  per 
cent,  overload  for  1  minute,  immediately  following  the  full-load 
run,  without  injury. 

To  obtain  this  rating  the  standard  open  motor  is  given  about 
twice  its  normal  rating. 

A  crane  motor  is  operated  with  brushes  on  the  neutral  position. 

Hoisting  Rating,  Open  Series  Motor. — For  such  service  the 
usual  temperature  guarantee  is  that — the  temperature  rise  shall 
not  exceed  55°  C.  after  a  full-load  run  for  1  hour,  the  machine 
shall  also  carry  50  per  cent,  overload  for  1  minute,  immediately 
following  the  full-load  run,  without  injury. 

To  obtain  this  rating  the  standard  open  motor  is  given  about 
twice  its  normal  rating. 

A  hoist  motor  is  operated  with  the  brushes  on  the  neutral 
position. 

Variable  Speed  Motors  for  Machine  Tools. — The  size  of  such  a 


MOTOR  DESIGN  AND  RATINGS  137 

machine  depends  on  the  minimum  speed  at  which  it  is  necessary 
to  give  the  rated  power  because  a  machine  tool  such  as  a  lathe 
takes  a  constant  horse-power  at  all  speeds,  since  the  cutting 
speed  of  the  tool  is  practically  constant.  After  the  minimum 
speed  has  been  fixed  the  maximum  speed  is  that  at  which  the 
peripheral  velocity  or  the  reactance  voltage  becomes  too  high. 
If  the  limit  of  speed  due  to  reactance  voltage  is  reached  before 
the  peripheral  velocity  of  the  machine  has  become  dangerous 
then  higher  speeds  can  be  obtained,  and  therefore  the  speed 
range  of  the  machine  increased,  by  the  use  of  interpoles. 


CHAPTER  XIV 
LIMITATIONS  IN  DESIGN 

109.  Relation  between  Reactance  Voltage  and  Average  Volts 

per  Bar.  —  The  voltage  between  brushes  =  Z6a  T-~^  X  --    ^-  10~8 

60        paths 

o 

and  the  number  of  commutator  segments  between  brushes   =  — 

for  both  series  and  multiple  windings,  therefore, 

the  average  voltage  between  adjacent  commutator  segments 


paths 

fcL 
ot"1* 

Thereactance  voltage  = 


-2TSCB  fcL      -P.m.     poles  vPolesxlO- 
Vot"1*)     60     XX~ 


patns 

where  k  —  0.93  for  short-pitch  multiple  windings,  Art.  69,  page  84. 
=  1.6  for  series  and  for  full-pitch  multiple  windings, 

therefore  average  volts  Per  segment  =  2Bg</>pr 
reactance  voltage  60kSIcT 


60/cg 

(22) 


110.  Limitation  Due  to  High  Voltage.  —  A  given  frame,  includ- 
ing yoke,  poles  and  armature  parts,  has  to  be  wound  for  different 
voltages  but  for  the  same  speed,  it  is  required  to  find  out  if  there 
is  any  upper  limit  to  the  voltage  for  which  the  machine  may  be 
wound. 

Since,  as  shown  in  Art.  109, 

average  volts  per  segment      B  Q(b 

—rr-  -  =  T^T  =  a  constant,  approx. 

reactance  voltage  I5qk 

therefore,  for  the  same  reactance  voltage  in  each  case,  the  average 
volts  per  segment  must  be  constant  and  the  number  of  commu- 
tator segments  must  increase  directly  as  the  terminal  voltage. 

As  the  number  of  commutator  segments  increases  the  thickness 
of  each  decreases  and  the  commutator  becomes  expensive  and 

138 


LIMITATIONS  IN  DESIGN  139 

is  liable  to   develop   high  bars,  since   the  probability  of  such 
trouble  increases  with  the  number  of  segments. 

When  the  point  is  reached  beyond  which  it  is  not  considered 
advisable  to  increase  the  number  of  commutator  segments, 
higher  terminal  voltages  must  be  obtained  by  an  increase  in  the 
number  of  turns  per  coil  or  by  a  decrease  in  the  number  of  paths 
through  the  winding  since 


=  a  constant  X  —  TT—    for  a  given  frame  and  speed, 
patns 

ST 

=  a  constant  X  —  TT~    for  a  given  frame  and  speed. 
paths 

In  either  case  the  average  volts  per  bar  is  increased  and  so  also  is 
the  reactance  voltage;  a  point  will  finally  be  reached  beyond 
which  the  reactance  voltage  becomes  so  high  that  good  commuta- 
tion is  impossible  without  the  use  of  interpoles. 

When  interpoles  are  supplied  the  voltage  between  commutator 
segments  may  have  any  value  up  to  about  30  if  the  load  is 
fairly  steady,  but  when  such  a  value  is  reached  the  machine 
becomes  sensitive  to  changes  of  load  and  liable  to  flash  over; 
the  limit  can  be  extended  a  little  further  by  the  use  of  com- 
pensating windings  as  described  in  Art.  77,  page  95,  but  very 
little  is  known  regarding  the  operation  of  D.-C.  machines  under 
such  extreme  conditions. 

111.  Limitation  due  to  Large  Current.  —  When  the  voltage  for 
which  a  machine  is  wound  is  lowered,  the  current  taken  from 
the  machine  increases  and  to  carry  this  current  increased  brush 
contact  surface  must  be  supplied. 

When  the  brushes  are  shifted  forward  so  as  to  help  commuta- 

pole  pitch     commutator  dia. 

tion  the  maximum  brush  arc  =  —  —  ~  --  X—  -~r-  --  and 

12  armature  dia. 

when  this  value  of  brush  arc  has  been  reached  increased  current 
can  be  collected  from  the  machine  only  by  increasing  the  axial 
length  of  the  brushes  and  commutator. 

The  commutator  bars  are  subject  to  expansion  and  to  con- 
traction as  the  load,  and  therefore  their  temperature,  varies,  and 
the  difficulty  in  keeping  a  commutator  true  increases  with  its 
length.  The  limit  of  commutator  length  must  be  left  to  the 
judgment  of  the  designer  since  it  varies  with  the  type  of  con- 
struction used  and  with  the  class  of  labor  available.  The  type 


140  ELECTRICAL  MACHINE  DESIGN 

of  commutator  shown  in  Fig.  28  is  seldom  made  longer  than 
24  in.;  longer  commutators  have  been  made  by  putting  two 
such  commutators  on  the  same  shaft  and  connecting  the  cor- 
responding bars  on  each  with  flexible  links  so  as  to  form  an 
equivalent  single  bar  of  twice  the  length. 

The  brush  arc  can  be  increased  about  20  per  cent,  over  the 
value  given  in  the  above  formula  if  the  brushes  are  in  the  neutral 
position,  and  low  resistance  brushes  may  be  used,  but  neither  of 
these  changes  can  be  made  unless  the  reactance  voltage  of  the 
machine  is  low  or  interpoles  are  supplied  to  take  care  of  the 
commutation;  such  low  resistance  brushes,  as  pointed  out  in 
Art.  64,  page  78,  have  a  larger  current  carrying  capacity  than 
have  brushes  of  higher  contact  resistance. 
112.  The  Best  Winding  for  Commutation. 

E,  the  generated  volt  age  =  Z^,ar 


patns 

r.p. 

1(f)a    60 

and  the  reactance  voltage 


_  r.p.m.   poles 

1(f)a    60      paths  X 


paths 

where  /c  =  1.6  for  series  and  full-pitch  multiple  windings 
=  0.93  for  short-pitch  multiple  windings 

therefore  the  reactance  voltage 

=  k  (SX  TX  r.p.m.  X^^-XlO"8)  ICLCT 
pains 


^   kT 
X 


paths 

For  a  given  frame  and  a  given  output  <f>aj  Lc  and  Exla  are  all 
constant  and  under  these  conditions 

A:  X  turns  per  coil 

Reactance  voltage •=  a  constant  X  -  -rr~ 

paths 

therefore  the  multiple  winding  is  better  than  the  series  winding 
since  it  has  the  larger  number  of  paths;  the  multiple  winding 
with  one  turn  per  coil  is  the  best  type  of  full-pitch  winding;  and 
the  short-pitch  multiple  winding  is  better  than  the  full-pitch 
multiple  winding  because  it  has  a  lower  value  of  k. 


LIMITATIONS  IN  DESIGN  141 

The  best  winding  that  can  be  used  in  any  case  is  therefore  the 
short-pitch,  one-turn  multiple  winding. 

113.  .  Limitations  due  to  Speed  in  Non-interpole  Machines.— 
The  best  winding  that  can  be  used  in  such  a  machine  is  the  short- 
pitch,  one-turn  multiple  winding  for  which  the  reactance  voltage 
-0.93  S  r.p.m.  ICLCIQ-8 
and  Ia=IcX  paths 

_  _  RV 

0.93XSXr.p.m.XLcXlO-8Xpa 


=  2  S(Bg(/frLc)    ':!'Q  'XlO~8-  for  a  one-turn  short-pitch 

multiple  winding,  since  poles  =  paths. 
therefore 


9  <UR  tlrrT  ^r-p'm<yin-8y  #7  X  paths 

=  2  S(BLc)  ~-  X 


o.93XSXr.p.m.xLcXlO-« 

RVxBgX</>XDa      . 

since  pT  =  xDa 
y 

watts  X  9      .  .    u  ,,.  , 

and  Da=  r>T/     p  v  ,    f°r   a     short-pitch,     one-turn     multiple 

K  V   /\  -D  g  X   Y 

winding. 

For  sparkless  commutation  from  no-load  to  25  per  cent. 
overload,  with  brushes  shifted  from  the  neutral  and  clamped, 
the  reactance  voltage  at  full-load  for  a  short-pitch  multiple 
winding  should  not  exceed  0.75  (volts  drop  per  pair  of  brushes), 
formula  H,  page  119,  and  the  volts  drop  per  pair  of  brushes 
should  not  exceed  3,  otherwise  it  will  be  difficult  to  keep  the 
commutator  cool,  therefore  the  highest  value  for  RV  in  the 
above  formula  is  0.75  X  3  =  2.25  volts;  for  this  value  the  armature 
diameter 

watts 

D-=5p<?x4 

=  —  B  —  X  6  approximately  for  a  short-pitch 

**g 

one-turn  multiple  winding  and  this  is  the  minimum  diameter 
that  can  be  used  for  the  output  without  the  risk  of  trouble  due 
to  commutation. 

Since  Bg  depends  principally  on  the  diameter  of  the  machine, 
as  shown  in  Fig.  89,  it  is  possible  to  plot  the  relation  between 


142 


ELECTRICAL  MACHINE  DESIGN 


output  in  watts  and  the  smallest  diameter  of  machine  from 
which  that  output  can  be  obtained  without  sparking  and  without 
the  use  of  additional  aids  to  commutation.  This  relation  is 
plotted  in  curve  1,  Fig.  95. 

In  order  to  use  a  smaller  diameter  than  that  given  by  the 
above  equation  it  is  necessary  to  use  a  higher  value  for  the  re- 
actance voltage  and  under  these  conditions  sparking  is  liable  to 
occur  unless  interpoles  or  some  other  device  is  used  to  help 
commutation. 


3000 


2500 


Curve  1  -     Armature  Dia.  in  Inches 

for  Non-Interpole  Machines 
2-  R.P.M.for  Non-Interpole  Machines 
3-R.P.M.for  Interpole  Machines 


2000 


1500 


1000 


500 


20     40     60     80    100 

Armature  Dia.  in  Inches 
600    1000   1500    2000   2500 
R.P.M. 

FIG.  95. — Limits  of  output  for  D.-C.  generators. 

114.  Limit  of  Output  for  Non-interpole  Machines. — The  pe- 
ripheral velocity  of  a  D.-C.  armature  should,  if  possible,  be  kept 
below  the  value  of  6000  ft.  per  minute,  because  for  higher  pe- 
ripheral velocities  the  cost  of  the  machine  increases  rapidly,  due  to 
the  difficulty  in  holding  the  coils  of  the  armature  against  cen- 
trifugal force. 

Taking  the  relation  between  minimum  diameter  of  armature 
and  output  plotted  in  Fig.  95,  and  a  maximum  peripheral  velocity 
of  6000  ft.  per  minute,  the  maximum  output  that  can  be  obtained 
for  a  given  speed  in  r.p.m.  is  figured  out  and  plotted  in  curve  2, 
Fig.  95. 

115.  Limit  of  Output  for  Interpole  Machines. — It  has  been 
shown  in  Art.  109,  page  138,  that 


LIMITATIONS  IN  DESIGN  143 

average  volts  per  bar_B^ 
reactance  voltage    ~  15qk 

where    &  =  1.6  for  a  full-pitch  multiple  winding,  the  type  used 
for  interpole  machines. 

The  average  voltage  between  commutator  bars  should  not 
exceed  30,  so  that  the  reactance  voltage,  even  for  interpole 
machines,  should  not  exceed  the  value 

PT7_30Xl5XgXl.6 

~B^xiT 

_1000Xg 
~B-g~ 

since  this  work  is  only  approximate  average  values  for  Bg  and 
for  q  may  be  used, 

if  50  =  55,000  lines  per  square  inch 

and  q    =800 

then  the  maximum  reactance  voltage  RV  =  15. 

It  was  shown  in  the  last  Art.  that  for  a  short-pitch  multiple 
winding  the  minimum  armature  diameter 

watts  X9 


in  the  same  way  it  can  be  shown  that  for  a  full-pitch  multiple 
winding  the  minimum  armature  diameter 

_  watts  X 15. 5 
a    RVxBgX</> 

the  difference  in  the  constant  being  due  to  the  fact 
that  k  for  a  short-pitch  winding  =  0.93 
whereas  k  for  a  full-pitch  winding  =  1.6. 

For  an  interpole  machine  the  reactance  voltage  should  not 
exceed  15  and  the  pole  enclosure  should  be  about  0.65;  for  these 
values 

_  watts  XI.  6 

Taking  this  value  of  Da,  a  peripherial  velocity  of  6000  ft.  per 
minute,  and  the  relation  between  Da  and  Bg  shown  in  Fig.  89 : 
the  maximum  output  that  can  be  obtained  for  a  given  speed  is 
figured  out  and  plotted  in  curve  3,  Fig.  95. 

116.  Limit  of  Output  for  Turbo  Generators. — The  only  differ- 
ence between  turbo  generators,  and  the  ordinary  interpole 
machine  discussed  in  the  last  article,  is  that  the  construction  of 


144 


ELECTRICAL  MACHINE  DESIGN 


the  former  is  made  such  that  it  can  be  run  at  peripheral  velocities 
of  the  order  of  15,000  ft.  per  minute. 

For  this  peripheral  velocity  and  for  a  reactance  voltage  of  15, 
the  maximum  output  that  can  be  obtained  for  a  given  speed 
is  figured  out  and  plotted  in  curve  1,  Fig.  96. 

Curve  2,  Fig.  96,  gives  the  usual  speed  of  steam  turbines  for 
different  outputs,  and  it  may  be  seen  that  for  outputs  greater  than 
1000  kw.,  it  is  difficult  to  build  generators  that  can  be  direct 
connected  to  steam  turbines,  because  speeds  lower  than  those  in 
curve  2  can  be  obtained  only  by  a  sacrifice  of  efficiency. 

The  output  for  a  given  speed  can  be  increased  over  the  value 
given  in  curve  l,Fig.  96,  by  the  use  of  peripheral  velocities 


3000 


2000 


1000 


1000   2000   3000   4000    5000  6000 
R.P.M. 

FIG.  96. — Limits  of  output  for  D.-C.  turbo-generators. 


higher  than  15,000  ft.  per  minute  and  by  the  use  of  a  higher  value 
of  the  average  volts  per  bar.  To  increase  that  value  over  30 
volts  will  probably  require  the  use  of  compensating  windings  in 
addition  to  interpoles  and  machines  have  been  built  in  which 
this  value  was  as  high  as  60  but  such  machines  are  very  sensitive 
to  changes  in  load  and  to  changes  in  the  interpole  field.  For 
such  a  high  value  of  average  volts  per  bar  the  reactance  voltage 
will  probably  be  about  30  volts  and  the  interpole  difficult  to 
adjust  and  further,  any  lag  of  the  interpole  field  behind  the  inter- 
pole current,  when  the  load  and  therefore  the  current  changes, 
will  lead  to  trouble  in  commutation. 

One  must  be  careful  in  the  interpretation  of  the  curves  shown 


LIMITATIONS  IN  DESIGN  145 

in  Figs.  95  and  96.  They  are  derived  on  the  assumption  that  the 
machine  is  limited  only  by  commutation.  For  many  of  the  out- 
puts within  the  range  of  the  different  curves  the  voltage  or  current 
limitation  might  be  reached  before  the  output  limit  is  reached 
due  to  speed.  Some  of  the  ratings  also  would  probably  require 
a  machine  with  forced  ventilation. 


10 


CHAPTER  XV 
DESIGN  OF  INTERPOLE  MACHINES 

117.  Preliminary  Design. — The  preliminary  design  work  on 
an  interpole  machine,  whereby  the  principal  dimensions  are 
determined  approximately,  is  carried  out  in  the  same  way  as 
that  on  the  non-interpole  machine  discussed  in  Art.  101,  page  120, 
but  some  slight  modifications  are  made  on  the  constants  used. 

It  was  pointed  out  in  Art.  66,  page  80,  that,  the  deeper  the  slots 
in  a  D.-C.  machine,  the  greater  the  slot  leakage  flux,  and  therefore 
the  greater  the  reactance  voltage;  because  of  this  the  slots  in 
non-interpole  machines  have  to  be  limited  in  depth  so  that  the 
value  of  q,  the  ampere  conductors  per  inch,  cannot  greatly 
exceed  that  given  in  Fig.  90.  When  interpoles  are  supplied 
the  reactance  voltage  becomes  of  less  importance  and  it  is 
possible  to  use  deep  slots  without  the  risk  of  trouble  due  to  poor 
commutation;  with  such  deep  slots  a  large  amount  of  copper 
can  be  put  on  each  inch  of  the  armature  periphery,  so  that  the 
value  of  q  may  be  made  larger  than  in  the  case  of  the  non-inter- 
pole machine,  and  is  usually  about  20  per  cent,  larger  than 
that  given  in  Fig.  90,  page  115. 

field  amp. -turns  per  pole  for  tooth  and  gap  .       ,  . 
The  ratio  -  -^r-        -  is  seldom 

armature  ampere-turns  per  pole 

less  that  1.2  for  machines  without  interpoles,  in  order  that  the 
magnetic  field  under  the  pole  tip  toward  which  the  brushes  are 
shifted  to  help  commutation  may  not  be  too  weak.  When  inter- 
poles are  supplied  such  a  commutating  field  is  no  longer  necessary, 
and  a  weaker  main  field  is  generally  used.  Inspection  of  Fig. 

49,  page  57,  will  show  that  if  the  cross-magnetizing  ampere-turns 

% 

at  the  pole  tips,  namely  J^—  IC}  becomes  equal  to  the  ampere- 
turns  per  pole  for  tooth  and  gap  due  to  the  main  field  excita- 
tion, then  the  effective  m.m.f .  across  the  gap  and  tooth  under  one 
pole  tip  will  be  zero  while  that  under  the  other  pole  tip  ha\e 
twice  the  no-load  value;  the  field  will  therefore  be  greatly 
distorted.  On  account  of  the  saturation  of  the  teeth  under 
this  latter  pole  tip  the  flux  density  will  not  be  proportional 
to  the  m.m.f.  and,  as  pointed  out  in  Art.  48,  the  total  flux  per 

146 


DESIGN  OF  INTERPOLE  MACHINES  147 

pole  will  be  reduced.  Due  to  the  high  flux  density  under  the  one 
pole  tip,  the  armature  core  loss,  which  depends  on  the  maximum 
density  in  the  core,  will  be  higher  at  full-load  than  at  no-load, 
and  the  tendency  to  flash  over,  which,  as  pointed  out  in  Art.  77, 
page  95,  depends  principally  on  the  voltage  between  adjacent 
commutator  segments  at  any  point,  will  also  be  greater. 

„,  .    field  amp. -turns  per  pole  for  tooth  and  gap  . 

The  ratio  -  '-±  is  found 

armature  cross  ampere-turns  at  the  pole  tips 

in  practice  to  have  a  value  of  about  1.2  for  interpole  machines 
and,  taking  the  value  of  the  pole  enclosure  =  0.65,  the  ratio 
field  amp. -turns  per  pole  for  gap  and  tooth 

armature  ampere-turns  per  pole 

=  0.8  approx. 

As  the  armature  ampere-turns  per  pole  is  increased  the  field 
ampere-turns  must  increase  in  the  same  ratio,  and  the  pole 
length  must  also  increase  in  order  to  carry  this  excitation.  When 
the  armature  strength  reaches  the  value  of  10,000  ampere-turns 
per  pole  it  will  generally  be  found  that  an  increase  in  the  number 
of  poles,  and  therefore  a  decrease  in  the  armature  strength  per 
pole  and  in  the  length  of  poles,  will  give  a  more  economical 
machine. 

„,          .     magnetic  loading     Bg</>Lc 

The  ratio  — r^^— i — 3-=—-  •  =—          ,  Art.  99,  page  116,  and 
electric  loading  q 

for  interpole  machines  is  generally  about  10  per  cent,  smaller  than 
for  machines  without  interpoles;  in  the  above  equation  <p  is 
slightly  less  to  give  room  for  the  interpoles  and  q,  as  pointed  out 
above,  is  generally  20  per  cent,  greater. 

118.  Example  of  Preliminary  Design. — The  machine  to  be 
taken  as  an  example  of  interpole  design  has  a  rating  that  lies 
within  curve  2,  Fig.  95,  that  is,  it  can  be  built  without  interpoles. 
In  order  to  compare  the  interpole  machine  with  that  which  has 
no  interpoles  two  designs  are  given  which  were  built  for  the 
same  rating;  the  non-interpole  machine  is  the  oldest. 

Example. — Determine  approximately  the  dimensions  of  a 
D.-C.  non-interpole  machine  of  the  following  rating:  200  kw.; 
115  volts,  no-load;  115  volts  full-load;  1740  amp.;  500  r.p.m. 

The  work  is  carried  out  in  tabular  form  as  follows: 

Ampere  conductors  =0.64X  10s,  from  Fig.  91. 

Ampere  conductors  per  inch  =660,  from  Fig.  90. 

Armature  diameter  =31  in. 

Apparent  gap  density  .80  =  53,000    lines    per   square   inch, 

from  Fig.  89. 


148 


ELECTRICAL  MACHINE  DESIGN 


Frame  length 

Poles 

Pole  pitch 

Flux  per  pole 

Total  face  conductors 

Winding 

Reactance  voltage 

Commutator  diameter 

Brush  arc 

Brush  length 


Lc  =  10  in.;  formula  B,  page  119. 
p  =  6;  formula  C  . 
T  =  16.2  in. 


Z  =  230,  formula  D. 

one-turn  multiple,  short  pitch. 
RV  =  1.55;  formula  G. 

=  0.  6  X  armature  diameter  =  19  in. 
=  0.83;  formula  P. 
=  20  in. 


Amperes  per  square  inch  brush  contact  =  35 

This  commutator  will  be  very  long  and  will  probably  give 
trouble;  the  length  can  be  reduced  by  increasing  the  diameter 
so  as  to  allow  the  use  of  a  wider  brush.  In  the  actual  machine 
the  commutator  diameter  was  made  21  in.;  the  brush  arc  was 
made  1  in.,  which  is  10  per  cent,  larger  than  the  value  obtained 
by  the  use  of  formula  P,  page  120,  and  was  possible  because 
the  reactance  voltage  is  low;  the  brush  length  was  cut  down 
to  16  in.,  for  which  brush  and  commutator  the  amperes  per 
square  inch  of  brush  contact  is  36. 

The  final  designs  for  both  the  interpole  and  the  non-interpole 
machine  are  given  in  the  following  partial  design  sheet. 

119.  Armature  and  Commutator  Design  Sheet. — All  in  inch 
units. 


Armature. 


Ex.  diameter  

31 

26 

In.  diameter  

20 

14.5 

Frame  length  
End  ducts 

10 

14 

Center  ducts  
Gross  iron 

2-1 
9 

4-f 
12.5 

Net  iron 

8.1 

11.2 

Slots,  number  

120 

120 

Slots,  size  

0.4X1.34 

0.33X2 

Oond.  per  slot,  num- 
ber 

2 

2 

Cond.  per  slot,  size  . 
Coils 

2(0.12X0.5) 
120 

2(0.1X0.75) 
120 

Turns  per  coil  

1 

1 

Total  conductors.  .  . 

240 

240 

Winding,  type  

Multiple. 

Multiple. 

Winding,  pitch  

J  Short  \ 
1  1-20  J 

1  1-21  f 

Slot  pitch  

fO.SlJ 

10.74J 

/0.68    1 
10.578J 

Tooth  width 

J0.41J 

fO.35    I 

Max.  tooth  width 

10.34J 
1  02 

10.248J 
1  .06 

Slot  width 
Core  depth  

4.16 

3.75 

Commutator. 

Diameter 21  21 

Face 19  16| 

Bars 120  120 

Bars  and  mica.  ...   0.55  0.55 

Brush  arc 1.0  1.15 

Brush  studs 6  6 

Brushes  per  stud .   9(fXlf)  8(lXlf) 
Amp.    per    square 

inch  contact 36  36 

Perip.  velocity 2750  2750 

Friction  loss 3250  3250 

Volts  per  pair  of 

brushes 2.5  2.0 

Contact  resistance 

loss 4350  3500 

Watts  per  square 

inch  surface. ...    6  6 

Temperature  rise.    45° C.  45° C. 
Average  volts  per 

bar.... 5.75  5.75 

Copper  loss,  Commutation. 
Amp.     cond.     per 

inch 710  850 

Cir.  mils  per  amp.   500  620 


DESIGN  OF  INTERPOLE  MACHINES 


149 


124 


5800 
0.83 
3.9 


5.75X10« 

Type  

Non- 

Interpole 

inter- 

160,000 

pole 

Rating. 

149,000, 

Poles 

6 

6 

70,000 

kw  

200 

200 

Volts  no-load  

115 

115 

46,500 

Volts  full-load.... 

115 

115 

25 

Amperes  

1740 

1740 

0.2 

r.p.m  

500 

500 

1.12 
3250 

Magnetic  loading 
Electric  loading 

500 

500 

1600 

Output  factor.  .  .  . 

4.15 

4.25 

Armature  Commutator 

Pole  pitch 16.2  13.6  Arm.  AT.  per  pole.  5800 

Per  cent,  enclosure .      0.7  0.65  •   .    AT. (gap  +  tooth) 

Min.  tooth  area  per  Ll°  arm.  AT.  per  pole 

pole 38.5  36  Reactance  voltage  1 .62 

Core  area  per  pole. .   33 . 6  42 

Apparent  gap   area 

per  pole 114 

Densities,  Iron  loss,  Excitation. 

Flux  per  pole 5.75X106 

Max.  tooth  density 

(apparent) 150,000 

Max.  tooth  density 

(actual) 141,000 

Core  density 85,000 

Gap  density,  (ap- 
parent)    50,500 

Frequency 25 

Air  gap  clearance.  .  0.3 

Carter  coefficient. .  .  1.12 

AT.  gap 5400 

AT.  tooth 1000 

The  reactance  voltage  in  each  case  is  figured  from  formula  G, 
page  119,  and  is  larger  for  the  interpole  than  for  the  non-interpole 
machine,  because  the  former  has  the  longer  fram3  length  and 
has  also  a  full- pitch  winding,  whereas  that  in  the  latter  machine 
is  short-pitch. 

The  actual  reactance  voltage  in  the  case  of  the  interpole 
machine  will  probably  be  greater  than  that  determined  from 
the  formula  because  the  coils  are  now  short  circuited  while  under 
the  interpole,  the  presence  of  which  lowers  the  reluctance  of  the 
path  of  that  part  of  the  leakage  flux  which  circles  the  short- 
circuited  coil  by  crossing  the  tooth  tips. 

120.  Design  of  the  Field  System  for  an  Interpole  Machine. — 
The  design  of  the  shunt  and  series  windings  presents  no  new 
problem  and  is  worked  out  in  the  same  way  as  that  of  the  field 
system  designed  in  Art.  57,  page  67. 

The  shunt  winding  is  usually  tapered,  as  shown  in  Fig.  97, 
so  that  the  air  has  free  access  to  all  the  field  coils. 

The  series  winding  is  supplied  to  give  the  necessary  compound- 
ing effect.  While  the  demagnetizing  ampere-turns  per  pole  in  an 
interpole  machine  is  zero,  since  the  brushes  are  on  the  neutral 
position,  yet  the  effect  of  the  cross  magnetizing  ampere-turns 
in  reducing  the  flux  per  pole,  see  Art.  49,  page  56,  is  large, 


because  the  ratio 


main  field  AT  for  gap  and  tooth 


armature  amp. -turns  per  pole 
the  field  distorsion  is  therefore  great. 


is  small  and 


150 


ELECTRICAL  MACHINE  DESIGN 


After  the  shunt  and  series  fields  are  designed  they  are  drawn 
in  to  scale,  as  shown  in  Fig.  97,  and  from  that  drawing  the  radial 
length  of  the  interpole  coil  space  is  determined,  and  then  the 
interpole  itself  is  designed  in  the  following  way: 

Example. — Design  the  interpole  and  its  winding  for  the 
machine  given  in  the  design  sheet  on  page  148. 

Lip,  the  axial  length  of  the  interpole,  is  found  from  the 
formula 


FIG.  97. — Field  windings  of  an  interpole  machine. 
,  48X? 


B 


ip 


page  94,  where  Bip  is  assumed  to  be  =  45, 000  lines  per  square 
inch. 

g=850,  from  design  sheet 
Lc  =  14  in.  from  design  sheet 
therefore  L;  p  =  1 2. 5  in. 

Wip  the  interpole  width  at  the  armature  surface,  is  found  from 
the  formula  Wip  +2^  =  brush  arc  +  slot  pitch  —  segment  width 
all  measured  at  the  armature  surface,  Art.  76,  page  93,  where 
the  brush  arc  referred  to  the  armature  surface 

=  brush  arc  X 


=  1.15X 
=  1.42  in. 


26 
2l 


and  slot  pitch  =  segment  width  at  the  armature  surface,  for  a 
machine  with  one  coil  per  slot. 


DESIGN  OF  INTERPOLE  MACHINES  151 

To  prevent  pulsation  of  the  interpole  field  the  effective  inter- 
pole  arc  should  be  approximately  a  multiple  of  the  slot  pitch; 
the  slot  pitch  =  0.68  in.  and  twice  the  slot  pitch  =  1.36  in., 
which  is  approximately  =  1.42  in.  The  effective  interpole  arc  is 
therefore  taken  as  1.4  in.  and  the  interpole  is  trimmed  down  at 
the  tip,  as  shown  in  Fig.  97,  so  that  the  actual  interpole  width 
at  the  tip 

=  effective  width  —  2$ 
=  1.4-0.4 
=  1  in. 

The  interpole  winding  has  now  to  be  designed. 
The  armature  amp. -turns  per  pole  =  5800 

The  interpole   amp. -turns  per  pole  =  5800X1. 5   approximately, 

Art.  76,  page  94. 

=  8700  approximately 

S7nn 

The  number  of  turns  required  on  each  interpole  =  s-yr-i — T — 

full-load  current 

=  5. 

The  full-load  current  is  1740  amperes,  and  to  carry  such  a 
large  current  very  heavy  copper  would  be  required  for  the  inter- 
pole winding,  the  winding  is  therefore  divided  into  two  circuits 
which  are  put  in  parallel  and  each  carries  half  of  the  total  cur- 
rent, namely  870  amperes;  each  coil  has  twice  the  number  of 
turns  found  above,  namely  10. 

The  external  surface  of  each  interpole  coil  =  external  periphery 
X  radial  length,  where  the  radial  length,  =7.5  in.,  is  taken  from 
Fig.  97  and  the  external  periphery  =  38  in.  approximately,  there- 
fore, the  external  surface  =  38  X  7.5  =  290  sq.  in. 

The  permissible  watts  per  square  inch  =  0.8,  from  Fig.  56,  page 
64,  and  this  is  increased  50  per  cent,  because  of  the  ventilated 
construction,  therefore  the  total  permissible  loss  per  coil 

=  290X0,8X1.5  =  350  watts. 

mean  turn  X  turns   per   coil  X  current2 

1  he  loss  in  each  coil  =  —  — • ^ —   —r- — 

cir.  mil.  section 

where  the  mean  turn  =  34  in.  approximately  and  the  current  =  870 

amperes,  therefore 

the  section  of  the  interpole  copper  in  cir.  mils 

mean  turn  X  turns  per  coil  X  current2 
loss  in  each  coil 


152  ELECTRICAL  MACHINE  DESIGN 

^34X10X8702 
350 

=  740,000 
—  0.58  sq.  in. 

The  actual  winding  was  made  with  10  turns  per  coil  of 
0.5  sq.  in.  section  made  up  of  ten  strips  each  =  0.1  m.  X0.5  in.  so 
that  it  could  easily  be  bent  to  shape.  The  section  was  a  little  less 
than  that  obtained  by  calculation  because  the  required  number 
of  ampere-turns  have  been  taken  slightly  larger  than  necessary; 
the  interpole  current  is  adjusted  after  the  machine  has  been  set 
up  for  test  by  means  of  a  shunt  in  parallel  with  the  interpole 
winding. 


CHAPTER  XVI 
SPECIFICATIONS 

121.  Specifications. — A  specification  for  an  electrical  machine 
is  a  detailed  statement  made  out  by  the  intending  purchaser 
to  tell  the  bidder  what  he  has  to  supply.  When  agreed  to  by 
both  buyer  and  seller  it  generally  forms  part  of  the  contract. 
The  following  is  a  typical  specification  for  a  D.-C.  generator. 

SPECIFICATION  FOR  A  DIRECT-CURRENT  GENERATOR 

Type. — Two-wire,  compound  wound,  non-interpole. 

Rating. — Rated  capacity  in  kilowatts 400 

No-load  voltage 240 

Full-load  voltage 240 

Normal  full-load  current 1670 

Speed  in  revolutions  per  minute 200 

Construction. — The  generator  will  be  of  the  engine  type  for 
direct  connection  to  a  steam  engine  and  shall  be  furnished 
without  shaft.  The  armature  core  and  the  commutator  shall 
be  built  together  on  a  cast-iron  spider  arranged  to  be  pressed  on 
the  engine  shaft. 

The  poles  shall  be  securely  attached  to  the  yoke  by  bolts,  and 
the  yoke  must  be  split  so  that  half  of  it  may  readily  be  removed 
if  necessary. 

Armature. — The  armature  shall  be  of  the  slotted  drum  type. 
Hardwood  wedges,  driven  into  grooves  in  the  teeth,  to  be 
used  to  retain  the  coils  in  the  slots  so  as  to  dispense  with  the 
use  of  band  wires  on  the  core.  The  armature  coils  shall  be 
formed  without  joints,  then  insulated  completely,  impregnated 
under  pressure,  pressed  in  heated  forms  and  cooled  under 
pressure.  The  winding  must  be  such  that  the  coils  are  all 
individually  removable  and  are  all  of  the  same  form  and 
dimensions. 

Commutator. — The  commutator  bars  shall  be  of  hard  drawn 
copper  and  must  be  insulated  from  one  another  by  mica  of  such 
quality  and  thickness  as  to  ensure  even  wear  on  the  commutator 
surface;  the  wearing  depth  of  the  commutator  must  be  not  less 
than  1  in.  The  ends  of  the  armature  conductors  shall  be  thor- 

153 


154  ELECTRICAL  MACHINE  DESIGN 

oughly  soldered  to  the  necks  of  the  commutator  bars.  All  bolt 
heads  and  other  projecting  parts  must  be  protected  in  such  a  way 
that  a  person  can  examine  the  brushes  without  the  risk  of  being 
caught. 

Brush  Holders  and  Supports. — Brush  holders  shall  be  designed 
for  carbon  brushes  and  so  constructed  as  to  give  ready  access 
to  the  commutator.  The  supports  which  carry  the  brush  hold- 
ers must  be  strong  and  rigid  and  constructed  so  that  they  may  be 
shifted  to  adjust  the  brushes  and  locked  in  any  desired  position. 

Workmanship  and  Finish. — The  workmanship  shall  be  first 
class.  All  parts  must  be  made  to  standard  gauges  and  be  inter- 
changeable. All  surfaces  not  machined  are  to  be  dressed,  filled 
and  rubbed  down  so  as  to  present  a  smooth  finished  appearance. 

Rheostat. — A  suitable  shunt-field  rheostat  of  the  enclosed 
plate  type  will  be  supplied. 

Pressing  on  Armature. — The  armature  will  be  pressed  on  the 
shaft  by  the  engine  builder  to  whom  the  generator  builder  will 
supply  an  accurate  gauge  of  the  diameter  of  the  armature  bore, 
the  engine  builder  to  make  the  allowance  for  press  fit. 

Keys. — Gauges  of  the  key  ways  in  the  armature  will  be  furnished 
by  the  generator  builder. 

Foundation  bolts  will  not  be  furnished. 

Bidders  shall  furnish  plans  or  cuts  with  descriptive  matter 
from  which  a  clear  idea  of  the  construction  may  be  obtained. 
They  shall  also  state  the  following: 
Armature  net  weight; 
Total  net  weight; 
Shipping  weight; 
Efficiency  at  1/4,  1/2,  3/4,  full,  and  1  1/4  load. 

The  Losses  shall  include  all  the  losses  in  the  machine  except 
windage  and  bearing  friction,  they  shall  also  include  the  loss 
in  the  shunt  field  circuit  rheostat,  and  in  the  series  shunt  should 
that  be  supplied. 

The  constant  armature  and  commutator  loss  will  be  found  by 
driving  the  machine  by  an  independent  motor,  the  output  of 
which  may  be  suitably  determined,  the  machine  being  run  at 
normal  speed  and  excited  so  as  to  generate  the  full-load  voltage  + 
the  voltage  drop  at  full-load  in  the  armature,  brushes  and  series 
field. 

The  shunt  field  coil  and  rheostat  loss  shall  be  taken  as  the 
terminal  voltage  X  the  no-load  exciting  current. 


SPECIFICATIONS  155 

The  armature  copper,  brush,  and  series  field  losses  will  be  found 
by  passing  currents  corresponding  to  the  different  loads  through 
the  armature  and  measuring  the  voltage  drop  so  as  to  include 
armature,  brushes  and  series  field,  the  armature  being  stationary. 
The  voltage  drop  X  the  corresponding  current  will  be  taken  as 
the  loss  in  these  parts,  this  test  to  be  made  immediately  after 
the  heat  run. 

Excitation. — The  shunt  excitation  must  be  such  that  the 
terminal  voltage  of  the  machine  at  full-load  may  be  raised  at  least 
15  per  cent,  above  normal  by  the  operation  of  the  shunt  field 
rheostat. 

Temperature. — The  machine  shall  carry  the  rated  capacity 
at  full-load  voltage  and  normal  speed  continuously,  with  a  tem- 
perature rise  that  shall  not  exceed  40°  C.  by  thermometer  on  any 
part  of  the  armature  or  commutator,  or  60°  C.  by  thermome- 
ter or  by  resistance  on  any  part  of  the  field  windings.  The 
machine  shall  also  carry  25  per  cent,  overload  at  normal  full-load 
voltage  for  two  hours,  immediately  following  the  full-load  run, 
without  the  temperature  rise  exceeding  55°  C.  by  thermometer 
on  any  part  of  the  armature  or  commutator  or  60°  C.  by 
thermometer  or  resistance  on  any  part  of  the  field  system. 

The  temperature  rise  should  be  referred  to  a  room  temperature 
of  25°  C. 

Commutation. — The  machine  shall  carry  continuously  any 
load  from  no-load  to  25  per  cent,  overload  without  destructive 
sparking  and  without  shifting  of  the  brushes. 

Insulation. — The  machine  shall  withstand  the  puncture 
test  recommended  in  the  standardization  rules  of  the  American 
Institute  of  Electrical  Engineers  and  the  insulation  resistance 
of  the  whole  machine  shall  be  greater  than  1  megohm. 

Testing  Facilities. — The  builder  shall  provide  necessary  fa- 
cilities and  labor  for  testing  in  accordance  with  this  specification. 

122.  Points  to  be  Observed  in  Writing  Specifications. — A 
specification  should  have  only  one  interpretation  and  should 
therefore  contain  no  such  general  clauses  as  perfect  commuta- 
tion or  satisfactory  operation,  because  these  terms  have  no 
generally  accepted  meaning. 

While  the  general  construction  of  the  machine  should  be 
described,  details  which  have  no  particular  effect  on  the  operation 
of  the  machine  should  not  be  embodied  in  a  specification  as 
they  merely  tend  to  prevent  competition  without  improv- 


156  ELECTRICAL  MACHINE  DESIGN 

ing  the  operating  qualities  of  the  machine,  but  were  certain 
details  such  as  form  wound  coils  are  desired  they  should  be 
specified. 

The  recommendations  of  the  Standardization  Rules  of  the 
American  Institute  of  Electrical  Engineers  should  be  followed  as 
closely  as  possible. 

Temperature  guarantees,  lower  than  those  in  general  use  for 
the  type  of  apparatus  on  which  the  specification  is  being  written, 
should  not  be  demanded  unless  absolutely  necessary.  If  it  is 
desired  that  the  rating  be  liberal,  it  is  better  in  most  cases  to 
call  for  a  machine  of  greater  capacity  than  that  corresponding  to 
the  proposed  load.  Manufacturers  build  standard  apparatus 
to  suit  the  average  trade,  and  such  a  standard  machine  can 
only  be  run  with  a  temperature  rise  below  normal  by  the  use 
of  low  resistance  brushes  to  keep  the  commutator  loss  down  and 
by  the  use  of  small  air  gaps  and  therefore  low  excitation  to  keep 
the  field  heating  down;  both  of  these  changes,  however,  tend  to 
make  the  commutation  poor,  so  that  the  machine  built  to  suit 
such  guarantees  is  often  liberal  so  far  as  heating  is  concerned 
but  closely  rated  so  far  as  commutation  is  concerned. 

The  figures  for  efficiency  should  be  left  for  the  maker  of  the 
machine  to  supply.  The  method  whereby  the  efficiency  shall 
be  calculated  should  be  stated.  In  the  case  of  engine  type 
generators  the  bearings  are  supplied  by  the  engine  builder  so 
that  the  bearing  friction  loss  cannot  readily  be  measured;  for 
that  reason  the  windage  and  bearing  friction  losses  are  not 
considered  in  calculating  the  efficiency  of  such  a  type  of 
machine. 

123.  Effect  of  Voltage  on  the  Efficiency. — If  two  machines  are 
built  on  the  same  frame,  and  for  the  same  output  and  speed,  but 
for  different  voltages,  the  losses  will  be  affected  in  the  following 
way. 

The  windage  and  the  bearing  friction  will  be  unchanged  since 
they  depend  on  the  speed,  which  is  constant. 

The  excitation  loss  will  be  unchanged  since  the  same  frame 
and  the  same  flux  per  pole  are  used. 

The  iron  loss  will  be  unchanged  since  the  flux  per  pole  is  the 
same  in  each  case  and  so  also  is  the  frequency. 

The  brush  friction  loss  will  be  the  lower  in  the  machine  with  the 
higher  voltage  because,  for  a  given  output,  the  current  to  be 
collected  from  the  commutator  is  inversely  as  the  voltage,  and 


SPECIFICATIONS  157 

the  brush  contact  surface  on  which  the  brush  friction  depends 
is  directly  proportional  to  the  current  to  be  collected. 

The  contact  resistance  loss  will  be  lower  in  the  machine 
with  the  higher  voltage  if  the  machines  are  wound  so  as  to  have 
the  same  reactance  voltage,  because  then  the  same  volts  drop 
per  pair  of  brushes  will  be  required  for  each  machine,  and  the 
contact  resistance  loss,  which  is  equal  to  the  volts  drop  per  pair 
of  brushes  X  the  full-load  current,  will  be  proportional  to  that 
current  and  so  inversely  proportional  to  the  terminal  voltage. 

The  armature  copper  loss  is  independent  of  the  voltage  if  the 
same  total  amount  of  armature  copper  is  used  in  each  case.  This 
may  be  shown  as  follows: 

Output  of  machine  =  volts  per  cond.  XZXlc 

LbXZXlc2 


and  armature  copper  loss  = 


M 

U 


MXZ 

Lb  (output) : 


MXZ     (volts  per  cond.) 

LbX  (output)2 

_  i  \  «>  /N 


(volts  per  cond.)2     total  copper  section 

=  a  const  ant  XT-  ~r-  — 

total  copper  section 

for  a  given  frame,  rating  and  speed. 

Except  in  the  case  of  very  small  machines,  the  same  amount  of 
copper  can  be  got  into  a  machine  at  any  voltage  up  to  600,  so 
that  over  this  range  the  higher  the  voltage  the  higher  the  effi- 
ciency, on  account  of  the  considerable  reduction  in  the  commuta- 
tor loss. 

124.  Effect  of  Speed  on  the  Efficiency.—  As  shown  in  Art,  97, 


page  114,  =  a  constant  X  Da2LcXBg  X  </>  X  q 

=  a  constant  X  Bg  X  q  for  a  given  frame. 
If  then  a  given  machine  is  increased  in  speed  the  frequency 
will  increase,  and  therefore  the  flux  per  pole,  and  Bg,  the  average 
flux  density  in  the  air  gap,  must  be  decreased,  as  shown  in  Art. 
92,  page  107,  while,  due  to  the  better  ventilation,  the  value  of  q 
must  be  increased  for  the  same  rise  in  temperature.  Over  a 
considerable  range  of  speed  the  product  of  Bg  and  q  is  approxi- 
mately constant  and  therefore  the  watts  output  is  approximately 
directly  proportional  to  the  r.p.m.  With  regard  to  the  losses;  the 


158 


ELECTRICAL  MACHINE  DESIGN 


field  excitation  loss  is  proportional  to  the  field  excitation  and, 
therefore,  as  shown  in  Art.  52,  page  61,  is  directly  proportional  to 

,  .  ,       Z/c       pole-pitch 
the  armature  ampere-turns  per  pole,  which  =-5— =g— 


2p 


2 

If  then 


and  so  for  a  given  machine,  is  directly  proportional  to  q. 
q  increases,  the  excitation  loss  also  increases. 

The  total  armature  and  commutator  loss  will  increase  with 
the  speed  because,  for  the  same  temperature  rise,  the  permissible 
loss  in  the  revolving  part  of  a  given  machine  =  (A  +  5Xr.p.m.) 
where  A  is  the  loss  that  is  dissipated  by  radiation  and  is  in- 
dependent of  the  speed. 

Thus  in  a  given  machine,  when  the  speed  is  increased,  the 
output  is  directly  proportional  to  the  speed,  the  excitation  loss  is 
increased  slightly,  and  part  of  the  armature  and  commutator  loss 
is  directly  proportional  to  the  speed,  therefore,  the  losses  do  not 


R.P.M.  Percent  Efficiency 

^ 

3^ 

~z=~- 

TT 

\ 

X® 

_ 

-&. 

— 

200       400        600       800     1000 
Kilowatts 

FIG.  98. — Efficiency  curves  for  550- volt  D.-C.  generators. 

increase  as  rapidly  as  the  output  does  and  the  higher  the  speed 
the  higher  the  efficiency  until  the  speed  is  reached  at  which  a 
radical  change  in  the  design  is  necessary,  such  as  the  addition 
of  interpoles  or  of  compensating  windings,  when  a  slight  drop 
is  efficiency  generally  takes  place  due  to  the  extra  loss  in  these 
additional  parts. 

If  now  the  case  be  taken  of  two  machines  which  have  the 
same  axial  length  and  the  same  pole-pitch  but  a  different  number 
of  poles,  and  the  speed  in  r. p.m.  is  made  inversely  as  the  number 
of  poles  so  that  the  peripheral  velocity  and  the  frequency  is  the 


SPECIFICATIONS 


159 


same  in  each  case,  then  each  pole,  with  the  corresponding  part 
of  the  armature,  may  be  considered  as  one  unit. 

The  output,  excitation  loss,  armature  and  commutator  loss 
will  all  be  proportional  to  the  number  of  poles,  so  that,  for  an 
increase  in  the  watts  output  with  a  proportional  decrease  in  the 
speed,  the  efficiency  is  unchanged  over  a  considerable  range  in 
speed. 

Curves  1  and  2,  Fig.  98,  show  the  efficiencies  that  may  be 
expected  from  a  line  of  550  volt  D.-C.  generators  at  speeds 


95 

w 

I     90 

£ 
'     85 


1000 


500 


0         20         40         60         80        100 
Horsepower 

FIG.  99. — Efficiency  curves  for  220-volt  D.-C.  motors. 


given  in  the  corresponding  speed  curves  1  and  2;  the  slow  speed 
machines  are  direct  connected  engine  type  units  and  the  efficiency 
does  not  include  the  windage  and  bearing  friction  losses;  the 
high-speed  machines  are  belted  units. 

Figure  99  shows  a  similar  set  of  curves  for  a  line  of  220  volt  D.-C. 
motors. 


CHAPTER  XVII 
ALTERNATOR  WINDINGS 

125.  Single-phase  Fundamental  Winding  Diagram. — Diagram 
A,  Fig.  100,  shows  the  essential  parts  of  a  single-phase  alternator 
which  has  one  armature  conductor  per  pole.  The  direction  of 
motion  of  the  armature  conductors  relative  to  the  magnetic 


\ 

^y 

o 

\ 
s 

J, 

^ 

y 

B 


N 


N 


FIG.  100. — Fundamental  single-phase  winding  diagram. 

field  is  shown  by  the  arrow,  and  the  direction  of  the  generated 
e.m.f.  in  each  conductor  is  found  by  Fleming's  three-finger  rule 
and  is  indicated  in  the  usual  way  by  crosses  and  dots. 

The  conductors  a,  6,  c  and  d  are  connected  in  series  so  that 
their  voltages  add  up  and  the  method  of  connection  is  indicated 

160 


ALTERNATOR  WINDINGS 


161 


in  diagram  A.  Such  a  connection  diagram,  however,  becomes 
exceedingly  complicated  for  the  windings  that  are  used  in 
practice  and  a  simpler  diagram  is  that  shown  at  C,  Fig.  100, 
which  is  got  by  splitting  diagram  A  at  xy  and  opening  it  out  on  to 
a  plane. 


FIG.  101. — Fundamental  two-phase  winding  diagram. 


FIG.   102. — Fundamental  three-phase  winding  diagram. 


Fl  n\  F. 

FIG.  103. — Fundamental  three-phase  Y-connected  winding. 

Diagram  C  may  be  called  the  fundamental  single-phase  wind- 
ing diagram  because  on  it  all  other  single-phase  diagrams  are 
based.  The  letters  S  and  F  stand  for  the  start  and  finish  of 
the  winding  respectively. 

126.  The  Frequency  Equation. — The  voltage  generated  in 
11 


162 


ELECTRICAL  MACHINE  DESIGN 


any  one  conductor  goes  through  one  cycle  while  the  conductor 
moves  relative  *to  the  magnetic  field  through  the  distance  of 
two-pole  pitches,  so  that  one  cycle  of  e.m.f.  is  completed  per  pair 
of  poles; 

/Y\ 

the  cycles  completed  per  revolution  =  y 

the   cycles  completed   per  second  =^  X  ']?'    > 

2*          oU 


Ph.  1 


Ph.  2 


Ph.  3 


A 


FIG.  104.  —  Currents  in  the  three  phases. 
therefore  /,  the  frequency  in  cycles  per  second 


120 


(23) 


127.  Electrical  Degrees. — The  e.m.f.  wave  of  an  alternator  is 
represented  by  a  harmonic  curve  and  therefore  completes  one 
cycle  in  2n  or  360  degrees;  as  shown  above,  the  e.m.f.  of  an 


Si 
FIG.  105. — Voltage  vector  diagram  for  a  Y-connected  winding. 

alternator  completes  one  cycle  while  the  armature  moves,  relative 
to  the  poles,  through  the  distance  of  two-pole  pitches;  it  is  very 
convenient  to  call  this  distance  360  electrical  degrees. 

128.  Two-  and  Three-phase  Fundamental  Winding  Diagrams. — 
Fig.  101  shows  the  fundamental  winding  diagram  for  a  two-phase 
machine.  A  two-phase  winding  consists  of  two  single-phase 
windings  which  are  spaced  90  electrical  degrees  apart  so  that  the 


ALTERNATOR  WINDINGS 


163 


e.m.fs.  generated  in  them  will  be  out  of  phase  with  one  another  by 
90  degrees. 

Figure  102  shows  the  fundamental  winding  diagram  for  a 
three-phase  machine.  A  three-phase  winding  consists  of  three 
single-phase  windings  which  are  spaced  120  electrical  degrees 
apart  so  that  the  e.m.fs.  generated  in  them  will  be  out  of  phase 
with  one  another  by  120  degrees. 


FIG.  106. — Fundamental  three-phase  A-connected  winding. 

129.  Y  and  A  Connection. — It  will  be  seen  from  Fig.  102 
that  a  three-phase  winding  requires  six  leads,  two  for  each  phase. 
It  is  usual,  however,  to  connect  certain  of  these  leads  together  so 
that  only  three  have  to  be  brought  out  from  the  machine  and 
connected  to  the  load. 


Ph.  1 


Ph.  2 


V 
/\ 


FIG.  107.— E.M.FS.  in  the  three  phases. 

Figure  103  shows  the  Y  connection  used  for  this  purpose.  The 
three  finishes  of  the  winding  are  connected  together  to  form  a 
resultant  lead  n  and  the  current  in  this  lead  at  any  instant  is  the 
sum  of  the  currents  in  the  three  phases.  The  current  in  each  of 
the  three  phases  at  any  instant  may  be  found  from  the  curves  in 


164  ELECTRICAL  MACHINE  DESIGN 

Fig.  104  from  which  curves  it  may  be  seen  that  at  any  instant  the 
sum  of  the  currents  in  the  three  phases  is  zero,  so  that  the  lead 
n  may  be  dispensed  with  and  the  machine  run  with  the  three  leads 
Slt  S2,  and  S3. 

Figure  105  shows  the  voltage  vector  diagram  for  a  Y-connected 
winding  and  from  the  shape  of  this  diagram  the  connection  takes 
its  name. 

Figure  106  shows  the  A  connection.  The  winding  is  connected 
to  form  a  closed  circuit  according  to  the  following  table: 

S,  to  F2 

52  to  Fs 

53  to  F! 

It  would  seem  that,  since  the  windings  form  a  closed  circuit,  the 
e.m.fs.  of  the  three  phases  would  cause  a  circulating  current  to  flow 


FIG.  108. — Voltage  vector  diagram  for  a  A -connected  winding. 

in  this  circuit;  however,  the  three  e.m.fs.  are  120  degrees  out 
of  phase  with  one  another  and  an  inspection  of  Fig.  107  will  show 
that  the  resultant  of  three  such  e.m.fs.  in  series  is  zero  at  any 
instant. 

Fig.  108  shows  the  voltage  vector  diagram  for  a  A  -connected 
winding,  the  phase  relation  of  the  three  voltages  is  the  same  as 
in  Fig.  105. 

130.  Voltage,  Current  and  Power  Relations  in  Y-  and  A  -Con- 
nected Windings. — Let  M  and  N,  Fig.  109,  represent  two  phases 
of  a  three-phase  winding,  the  voltages  generated  therein  are  out 
of  phase  with  one  another  by  120  degrees  and  are  represented 
by  vectors  in  diagram  B. 

If  the  phases  are  connected  in  series,  so  that  F2  is  connected 
to  Slf  then  the  voltage,  between  F1  and  S2  =  the  voltage  from 
F!  to  S±  +  the  voltage  from  F2  to  S2  =  Er,  diagram  C,  and 
is  equal  to  E,  the  voltage  per  phase. 


ALTERNATOR  WINDINGS 


165 


M  N 


I      Si       -F2     Sz 
A 


•3?, 


\ 


. 

FIG.  109. — Voltage  relations  in  three-phase  windings. 


M  N 


'* 


FIG.  110. — Current  relations  in  three-phase  windings. 


166 


ELECTRICAL  MACHINE  DESIGN 


If,  however,  as  in  a  Y-connected  winding,  F2  is  connected  to 
FU  then  the  voltage  between  St  and  S2  =  the  voltage  from 
S1  to  F±  4-  the  voltage  from  F2  to  S2  =  Er,  diagram  Z>,  which 
is  equal  to  1.73  E. 

In   a   Y-connected   machine   therefore,  the  voltage   between 


j-  — 

— 

1 

f  

. 

\ 

r  

""} 

C 

s 

'j 

{<  90°  * 

1 

A 

"'wo-phase 

f 

^ 

j 

i1 

> 

1! 

:'  i 

1 

k 
.    _1        k  

r 

/L  J 

-j-  A  ^ 

J 

c  t  -2  j 

^  T  ^ 

^       \ 

"1"T: 

.J   1 

•^2 

Ft 

i 

z? 

u 

m 


.m 


l<     12Q°  >j<    12Q2-»- 


Three-phase 


s, 


C  D 

FIG.  111. — Four-pole  chain  winding. 

terminals  is  1.73  times  the  voltage  per  phase,  while  the  current 
in  each  line  is  the  same  as  the  current  per  phase. 

Let  M  and  N}  Fig.  110,  represent  two  phases  of  a  three-phase 
winding,  the  currents  therein  are  out  of  phase  with  one  another 
by  120  degrees  and  are  represented  by  vectors  in  diagram  B. 


ALTERNA  TOR^W  IN  DINGS 


167 


If  the  two  phases  are  connectecfin  parallel,  so  that  F2  is  con- 
nected to  Flt  then  the  current  in  the  line  connected  to  F^F2  = 
the  current  from  Fl  to  S^  +  the  current  from  F2  to  S2  =  7r, 
diagram  C,  and  is  equal  to  I,  the  current  per  phase. 

If,  however,  as  in  a  A  -connected  winding,  S±  is  connected  to 
jP  then  the  current  in  the  line  connected  to  S  =  the  current 


FIG.  112. — Three-phase  chain  winding  with  one  slot  per  phase  per  pole. 


from  /Sj  to  F±  +  the  current  from  F2  to  >S2,  which  is  equal  to  the 
current  from  F2  to  S2  -  the  current  from  F^  to  S1  =  Ir,  diagram 
D,  =-1.737. 

In  a  A  -connected  machine  therefore,  the  current  in  each  line 
is  1.73  times  the  current  in  each  phase  while  the  voltage  between 
terminals  is  the  same  as  the  voltage  per  phase. 


168 


ELECTRICAL  MACHINE  DESIGN 


LL.JLJ  -  LL j 

I  I j i 


F,\ 


Two  Phase 


Three  Phase,  one  phase  shown 


FIG.  113. — Four-pole  double  layer  winding. 


ALTERNATOR  WINDINGS 


169 


The  power  delivered  by  a  three-phase  alternator 
=  3  E  I  cos  6 

=  1.73  Et  fi  cos  6  for  either  Y-  or  A -connected  machines 
where  E  is  the  voltage  per  phase, 
/  is  the  current  per  phase, 
Et  is  the  voltage  between  terminals, 
Ii  is  the  current  in  each  line, 
0  is  the  phase  angle  between  E  and  /. 

131.  Windings  with  Several  Conductors  per  Slot. — When  there 
are  more  than  one  conductor  per  slot  a  slight  modification  must 
be  made  on  the  fundamental  winding  diagrams.  Consider  for 
example  the  case  where  there  are  four  conductors  per  slot. 


FIG.  114. — Coil  for  a  double  layer  winding. 

One  method  of  connecting  up  the  winding  is  shown  in  Fig.  Ill, 
which  shows  the  two-  and  three-phase  diagrams.  Each  coil  m 
consists  of  four  turns  of  wire  as  shown  in  diagram  C;  these  wires 
are  insulated  from  one  another  and  are  then  insulated  in  a  group 
from  the  core  so  that  a  section  through  one  slot  and  coil  is  as 
shown  in  diagram  D.  On  account  of  its  appearance  this  type 
of  winding  is  called  the  Chain  Winding. 

Figure  112  shows  part  of  a  machine,  which  is  wound  according 
to  diagram  B,  Fig.  Ill;  the  method  whereby  one  coil  is  made  to 
jump  over  the  other  is  clearly  shown. 

Another  method  of  connecting  up  the  winding  is  shown  in 
Fig.  113,  which  shows  the  two-  and  three-phase  diagrams.  Each 


170 


ELECTRICAL  MACHINE  DESIGN 


coil  n  consists  of  two  turns  of  wire  as  shown  in  diagram  C; 
these  wires  are  insulated  from  one  another  and  are  also  insulated 
from  the  core  so  that  a  section  through  one  slot  and  coil  is  as 
shown  in  diagram  D. 

The  coils  are  shaped  as  shown  in  Fig.  114;  one  side  of  each 
coil,  represented  in  the  winding  diagrams  by  a  heavy  line,  lies 
in  the  top  of  a  slot,  while  the  other  side,  represented  by  a  light 
line,  lies  in  the  bottom  of  a  slot  about  a  pole-pitch  further  over 
on  the  armature.  The  whole  winding  lies  in  two  layers  and  is 
therefore  called  the  Double-Layer  Winding. 

132.  Comparison  between  Chain  and  Double-Layer  Windings. 


Chain 

The  number  of  conductors  per  slot 
may  be  any  number. 

The  number  of  coils  is  half  of  the 
number  of  slots. 

There  are  several  shapes  of  coil, 
therefore  a  large  outlay  is  neces- 
sary for  winding  tools,  and  a  large 
number  of  spare  coils  must  be  kept 
in  case  of  breakdown. 

The  end  connections  of  the  winding 
are  separated  by  large  air  spaces. 


Double-layer 

The  number  of  conductors  per  slot 
must  be  a  multiple  of  two. 

The  number  of  coils  is  the  same  as 
the  number  of  slots. 

The  coils  are  all  alike,  therefore  the 
number  of  winding  tools  is  a  min- 
imum and  so  also  is  the  number 
of  spare  coils  that  must  be  kept. 

The  end  connections  are  all  close 
together  and  therefore  more 
liable  to  breakdown  between 
phases  than  in  the  chain  winding. 


The  chain  winding  is  the  easier  to  repair  because,  in  order  to 
get  a  damaged  coil  out  of  a  machine,  fewer  good  coils  have  to  be 
removed  than  in  the  case  of  the  double  layer  winding;  this  may  be 
seen  from  the  chain  winding  and  the  corresponding  double- 
layer  winding  shown  in  Figs.  118  and  119. 

The  chain  winding  requires  the  larger  initial  outlay  for  tools 
but  the  winding  itself  is  the  cheaper  because  there  are  not  so 
many  coils  to  be  formed  and  insulated. 

The  amount  of  the  slot  section  that  is  taken  up  by  insulation  is 
less  with  the  chain  than  with  the  double-layer  winding,  as  may 
be  seen  by  comparing  diagrams  D,  Figs.  Ill  and  113. 

133.  Wave  Windings. — The  connections  from  coil  to  coil, 
marked/  in  diagram  A,  Fig.  113,  and  called  jumpers,  must  have 
the  same  section  as  the  conductors  in  the  winding.  When  there 
are  only  two  conductors  per  slot  the  conductors  are  large  in 
section  and  the  jumpers  become  expensive;  in  such  a  case  the 
wave  winding  is  generally  used  because  it  requires  very  few 


ALTERNATOR  WINDINGS 


171 


jumpers.     Such  a  winding  is  shown  in  Fig.  115,  which  shows  the 
two-  and  three-phase  diagrams. 

134.  Windings  with  Several  Slots  per  Phase  per  Pole. — Modern 
alternators  have  seldom  less  than  two  slots  per  phase  per  pole. 
The  principle  advantages  of  the  distributed  winding  are  that  the 
wave  form  is  improved  and  the  total  radiating  surface  of  the  coils 
increased;  the  self-induction  of  the  winding  is  reduced  but  that, 
as  shown  in  Art.  209,  page  282,  is  in  some  cases  a  disadvantage. 


Two  Phase 


Three  Phase 
FIG.  115. — Four-pole  wave  winding. 

135.  Windings  With  Several  Circuits  per  Phase. — The  windings 
shown  down  to  this  point  have  all  been  single-circuit  windings, 
that  is,  windings  in  which  all  the  conductors  of  one  phase  are 
connected  in  series  with  one  another.  It  is,  however,  often 
necessary  to  use  more  than  one  circuit. 

Suppose,  for  example,  that  a  large  number  of  small  alternators 
are  to  be  built  for  stock,  the  winding  used  would  be  such  that  by 


172 


ELECTRICAL  MACHINE  DESIGN 


a  slight  change  in  the  connections,  it  could  be  made  suitable  for 
a  number  of  standard  voltages. 


FIG.  116. — Two  circuit  windings. 


FIG.  117. — Alternator  with  an  eccentric  rotor. 

Figure  116  shows  the  winding  diagram  for  one  phase  of  an  eight- 
pole  three-phase  machine  with  two  slots  per  phase  per  pole. 


ALTERNATOR  WINDINGS 


173 


Diagram  A  shows  a  single  circuit  connection. 
Diagrams  B,  C  and  D  show  possible  two  circuit  connections. 
When  a  winding  is  divided  up  into  a  number  of  circuits  in 
parallel  it  is  necessary,  in  order  to  prevent  circulating  currents, 


Two  Circuit  , 

FIG.  118. — Four-pole,  two-phase,  chain  winding  with  eight  slots  per  pole. 


\     \ 

1 

1 

2               f 

IK 

$ 

m 

Two  Circuit 

Si 

FIG.   119. — Four-pole,   two-phase,   double  layer  winding  with  eight  slots 
per  pole,  one  phase  shown. 

that  the  voltages  in  the  different  circuits  in  parallel  be  equal 
to  and  in  phase  with  one  another. 

Diagram  B  does  not  meet  this  condition  because  the  voltages 
in  the  two  circuits  shown,  while  of  equal  value,  are  out  of  phase 


174 


ELECTRICAL  MACHINE  DESIGN 


--">""  ^      1 

f     7-- 

flit; 

Lj_j_j_ 

J 

i  i 

1    I                    \ 

M 

n 

_,        ,_ 

-3j~T 

~ 

—  ^—  —     ^_—  _ 

~ 

— 

T't: 

I 

i 
i 

1 

i 

»A°             •>     ^       "\n(\°\ 

1 

\f 

T 

& 

Is 

IT 

s, 

One  Circuit 


1 

1 

1 
1 

Fl 

3 

! 

k 

1^0 

5, 

One  Circuit  T 

Two  Circuit  Zik 


1^  i 

l« 

J      LJ 

i 
i 

u 

t 

(i 

k          1 

i 

—  4- 

-r~ 

^ 

s, 

Two  Circuit  Y 

FIG.  120. — ^Four-pole,  three-phase,  chain  winding  with  nine  slots  per  pole. 


ALTERNATOR  WINDINGS 


175 


|                pOOf                           XOO- 

T  jU^u^f-^      '            rvus'u'> 

1           1       J                   1 

1              J                                   M 

1 

| 

1 
US 

Fl 

|  IF. 

One  Circuit  y\ 

^                    1rtn°               ^     rf-                  1OA°                ^ 

<          laU  >•  •<  ±£(j  > 
o                        o 

03                                02                              * 

1 

\                                     1 

1 

1 

I 

1 

|F2 

Fl 

\&\ 

One  Circuit  Y 

\  c                      o 

1*^3                               02 

II  II  II  II  II 


r 

V^  ^  ^^  Y^  ^^    ^^  ^<7^'UVT  p                                    I    [^ 

')         *>                  '*!                  & 

w 

'      !       L     !            ffe 

I 

Si 

#1 

?                                     'o"2 

\s 

"^         15^3                                  1  0 

F 

~F* 

1  -j        ]5s 

\ 

r                               f 

I 

r                            '  j 

I 

i 

1 

& 

!j 

d  k      *; 

i 

i 

F 

1 

i 

s* 

„ 

Two  Circuit  Y 

FIG.   121. — Four-pole,  three-phase,  double  layer  winding  with  nine  slots 

per  pole. 


176 


ELECTRICAL  MACHINE  DESIGN 


with  one  another  by  the  angle  corresponding  to  one  slot-pitch, 
namely,  by  30  degrees. 

The  winding  shown  in  diagram  D  is  to  be  preferred  to  that  in 
diagram  C  for  the  following  reason.  Fig.  117  shows  an  eight-pole 
machine  the  field  and  armature  of  which  are  eccentric  due  to  poor 
workmanship  in  erection.  The  voltage  generated  in  a  circuit 
made  up  of  conductors  in  slots  a,  b,  c  and  d  is  smaller  than  that 


LL 


r 
I 

.,,,  i,  . 

—  —  . 

1 
i      j 

1      1 

1 

i  ! 

I     1 

i 

L    _|_ 

1 

1 

1 

J    L 

,«.l** 

FIG.  122. — Six-pole,   three-phase,  chain  winding  with  three  slots  per  pole. 

generated  in  a  similar  circuit  wound  in  slots  e,  /,  g  and  h,  so  that  if 
these  two  circuits  be  put  in  parallel  a  circulating  current  will 
flow.  Diagram  C,  Fig.  116,  shows  an  example  of  such  a  winding. 
In  diagram  D  the  connection  is  such  that  each  of  the  two 
circuits  takes  in  conductors  from  under  all  of  the  poles  so  that,  no 
matter  how  different  the  air  gaps  become,  the  voltages  in  the  two 
circuits  are  always  equal. 


L_—  -| 

•—  •> 

• 

1 

1 
i 
i 

•- 

j 

i 
L- 

—  -\ 

—. 

1 

"  1 

1  — 

FIG.  123. — Three-phase  chain  winding  with  coils  all  alike. 

136.  Examples  of  Winding  Diagrams. — Figs.  118, 119, 120  and 
121  show  typical  alternator  winding  diagrams  and  should  be 
carefully  studied.  Many  other  examples  might  have  been 
shown  but  the  subject  is  too  wide  to  take  up  in  greater  detail. 

When  the  number  of  groups  of  coils  is  odd  in  a  machine  with  a 
chain  winding,  it  is  impossible  to  have  the  same  number  of  groups 
of  long  as  of  short  coils,  and  one  group  must  be  put  into  the 
machine  the  coils  of  which  have  one  side  long  and  the  other 


ALTERNATOR  WINDINGS 


177 


side  short;  such  a  winding  is  shown  in  Fig.  122  for  a  six-pole 
machine  with  three  phases,  one  slot  per  phase  per  pole,  and  one 
coil  per  group. 

By  the  use  of  specially  shaped  coils,  as  shown  in  Fig.  123, 
it  is  possible  to  reduce  the  number  of  coil  shapes  that  are  re- 
quired for  a  chain  winding.  In  the  particular  case  shown 
the  coils  are  all  alike. 


Double  Layer  Winding 

FIG.  124. — Four-pole,  single-phase  winding  with  four  active  slots  per  pole. 

In  a  single-phase  machine  it  is  generally  advisable,  for  the 
reason  explained  in  Art.  145,  page  187,  to  make  the  winding 
cover  not  more  than  two-thirds  of  the  pole-pitch.  Such  a 
winding  is  shown  in  Fig.  124  for  a  machine  with  six  slots  per 
pole,  of  which  only  four  are  used. 


12 


CHAPTER  XVIII 
THE  GENERATED  ELECTRO -MOTIVE  FORCE 

137.  The  Form  Factor  and  the  E.M.F.  per  Conductor. 

If  (f>a  is  the  flux  per  pole 
and  p  the  number  of  poles 
then  one  armature  conductor  cuts  (f>ap  lines  of  force  per  revolution 

.       r.p.m.  r 
or  (f>ap     *        lines  per  second 

and  the  average  e.m.f.  in  one  conductor  =  (f)ap  -jr^ — :10~8  volts. 
The  form  factor  of  an  e.m.f.  wave  is  denned  as  the  ratio 


effective  voltage  .  .  \/2 

— r—  —  and  for  a  sine  wave  of  e.m.f.  this  value  =  7— 
average  voltage  2 


71 
1.11 


The  effective  e.m.f.  per  conductor  =  <£ap    '''  10~8  X  form  factor 

.m.f. 
(24) 


,       r.p.m. 
=  1.11  <£0p     ^        10~8for  sine  wave  e.m.f. 


,  ,  ,     . 
since  /,  the  frequency  = 

138.  The  Wave  Form.  —  Fig.  125  shows  the  shape  of  pole  face 
that  is  in  general  use  and  curve  A  shows  the  distribution  of  flux 
in  the  air  gap  under  such  a  pole  face.  ,  The  e.m.f.  in  a  conductor  is 
proportional  to  the  rate  of  cutting  lines  of  force  and  has  therefore 
a  wave  form  of  the  same  shape  as  the  curve  of  flux  distribution. 

Curve  A  is  not  a  sine  wave  but  can  be  considered  as  the 
resultant  of  a  number  of  sine  waves  consisting  of  a  fundamental 
and  harmonics.  The  frequency  and  magnitude  of  these  har- 
monics depend  principally  on  the  ratio  of  pole  arc  to  pole-pitch. 
In  Fig.  125  this  ratio  is  0.65  and  the  fundamental  and  harmonics 
which  go  to  make  up  the  flux  distribution  curve  are  shown  to 
scale,  higher  harmonics  than  the  seventh  being  neglected. 

178 


THE  GENERATED  ELECTRO-MOTIVE  FORCE    179 

139.  Trouble  due  to  Harmonics.  —  The  fundamental  and  har- 
monics that  go  to  make  up  an  e.m.f.  wave  act  as  if  each  had 
a  separate  existence.  If  the  circuit  to  which  this  e.m.f.  is  ap- 
plied consists  of  an  inductance  L  in  series  with  a  capacity  C 
so  that  the  impedence  of  the  circuit 


then  the  current  in  this  circuit  consists  of 


_  _ 

a  fundamental  =  1 

~2*AC 

En 


and  harmonics  of  the  form  ^  f  T         1 

nL<  — 


where  En  is  the  effective  value  of  the  nth  harmonic.     If  now,  fn 
has    such  a  value  that  2xfnL  =  so   that  the  circuit  is 


FIG.  125. — E.  M.  F.  wave  of  an  alternator. 

in  reasonance  at  this  frequency,  then  the  nth  harmonic  of  cur- 
rent will  be  infinite,  and  the  nth  harmonic  of  e.m.f.  across  L 
and  C  individually  will  also  be  infinite. 

The  above  is  an  ideal  case;  in  ordinary  circuits  the  current 
cannot  reach  infinity  on  account  of  the  resistance  that  is  always 
present,  nevertheless,  if  the  circuit  is  in  resonance  at  the  fre- 
quency of  the  fundamental  or  of  any  of  the  harmonics,  danger- 
ously high  voltages  will  be  produced  between  different  points  in 
the  circuit.  The  constants  of  a  circuit  are  seldom  such  as  to 


180 


ELECTRICAL  MACHINE  DESIGN 


give  trouble  at  the  fundamental  frequency,  trouble  is  generally 
due  to  high  frequency  harmonics.  It  is  desirable  then  to  elimi- 
nate harmonics  from  the  e.m.f.  wave  of  a  generator  as  far  as 
possible  and  several  of  the  methods  adopted  are  described  below. 
140.  Shape  of  Pole  Face. — The  pole  face  is  sometimes  shaped 
as  shown  in  Fig.  126,  that  is,  the  air  gap  is  varied  from  a  minimum 


FIG.  126. — Pole  face  shaped  to  give  a  sine  wave  e.  m.  f. 

under  the  center  of  the  pole  to  a  maximum  at  the  pole  tip,  so 
as  to  make  the  flux  distribution  curve  approximately  a  sine 
curve;  then  the  e.m.f.  wave  from  each  conductor  will  be  approxi- 
mately a  sine  wave. 

141.  Use  of  Several  Slots  per  Phase  per  Pole. — Fig.  127  shows 
part  of  a  three-phase  machine  which  has  six  slots  per  pole  or 


o    o     o 
A     B 


o    o     o     o 


FIG.  127. — E.  M.  F.  wave  of  a  three-phase  alternator  with  two  slots  per 

phase  per  pole. 

two  slots  per  phase  per  pole.  The  e.m.f.  generated  in  a  conductor 
in  slot  A  is  represented  at  any  instant  by  curve  A,  and  that  in  a 
conductor  in  slot  B  by  curve  B,  which  is  out  of  phase  with  curve  A 
by  the  angle  corresponding  to  one  slot-pitch,  or  30  degrees. 

When  the  conductors  in  slots  A  and  B  are  connected  in  series 
so  that  their  e.m.f s.  add  up,  the  resultant  e.m.f.  at  any  instant 
is  given  by  curve  C,  which  is  got  by  adding  together  the 
ordinates  of  curves  A  and  B.  C  is  more  nearly  a  sine  curve 
than  either  A  or  B.  -\ 

If  the  fundamental  and  harmonics  that  go  to  make  up  curves 


THE  GENERATED  ELECTRO-MOTIVE  FORCE    181 

A  and  B  are  known,  then  those  which  go  to  make  up  curve  C  can 
be  readily  found  as  follows:  The  fundamental  of  the  resultant 
wave  C  is  the  vector  sum  of  the  fundamentals  of  A  and  B,  which 
are  6  electrical  degrees  apart,  and  the  nth  harmonic  of  C  is  the 
vector  sum  of  the  nth  harmonics  of  A  and  B  which  are  (nX#) 


FIG.  128. — The  vector  diagram  for  the  fundamental  and  the  harmonics. 

electrical  degrees  apart.  For  example,  curves  A  and  B,  Fig.  128 
are  30  degrees  out  of  phase  with  one  another  and  each  consists 
of  a  fundamental  and  a  third  harmonic  as  shown.  Cj  is  the  re- 
sultant of  the  fundamentals  Al  and  B1  and  C3,  the  third  har- 
monic of  curve  C,  is  the  resultant  of  the  two  third  harmonics  A3 
and  B~. 


FIG.  129. — Short-pitch  coil. 

142.  Use  of  Short -pitch  Windings. — Fig.  129  shows  a  short- 
pitch  coil.  The  e.m.f.  waves  in  the  conductors  A  and  B  are  out 
of  phase  with  one  another  by  6  degrees,  but  each  has  the  same 
shape  as  the  curve  of  flux  distribution.  The  problem  of  finding 
the  resultant  e.m.f.  wave  is  therefore  the  same  as  that  discussed 
in  the  last  article. 


182 


ELECTRICAL  MACHINE  DESIGN 


If  n6,  the  phase  angle  between  the  nth  harmonics  of  curves 
A  and  B,  becomes  equal  to  180  degrees,  then  the  corresponding 
harmonic  is  eliminated  from  the  resultant  curve  C  since  the  two 


FIG.  130. — Elimination  of  harmonics  from  the  e.  m.  f .  wave. 


FIG.  131. — Unsymmetrical  waves  due  to  even  harmonics. 

harmonics  which  go  to  make  it  up  are  equal  and  opposite.  If,  for 
example,  there  are  9  slots  per  pole  and  the  coil  is  one  slot  short, 
then  the  angle  6  is  20  electrical  degrees,  and  the  9th  harmonic  is 
eliminated  from  the  voltage  wave  of  the  coil;  in  general,  if  the 


THE  GENERATED  ELECTRO-MOTIVE  FORCE    183 

pitch  of  the  coil  be  shortened  by  —  of  the  pole-pitch  then,  as 

shown  in  Fig.  130,  the  nth  harmonic  will  be  eliminated 

It  may  be  pointed  out  here  that  an  even  harmonic  is  seldom 
found  in  the  e.m.f .  wave  of  an  alternator,  because  the  resultant  of 
a  fundamental  and  an  even  harmonic  gives  an  unsymmetrical 
curve,  as  shown  in  Fig.  131,  where  the  resultant  curve  is  made  up 


D 
FIG.  132. — Effect  of  the  Y-  and  A -connection  on  the  third  harmonic. 


of  a  fundamental  and  a  second  harmonic.  If  then  the  e.m.f. 
wave  is  symmetrical  it  may  be  assumed  that  no  even  harmonics 
are  present. 

143.  Effect  of  the  Y-  and  A  -Connection  on  the  Harmonics. 
— The  fundamentals  of  the  three  e.m.fs.  are  120  degrees  out  of 
phase  with  one  another  and  are  represented  by  vectors  in  dia- 
gram A,  Fig.  132.  The  nth  harmonics  are  (nXl20)  degrees  out 
of  phase  with  one  another. 

When  the  -phases  are  Y-connected  the  terminal  F2  is  brought  to 
the  potential  of  terminal  F^  and  the  resultant  fundamental 


184  ELECTRICAL  MACHINE  DESIGN 

between  Sl  and  S2  is  represented  by  the  vector  S±S2  and  =1.73 
times  the  fundamental  in  one  phase.  In  the  case  of  the  third 
harmonic  the  e.m.fs.  are  (3  X 120)  =  360  degrees  out  of  phase  with 
one  another  and  are  represented  by  vectors  in  diagram  B; 
the  resultant  third  harmonic  between  Sl  and  S2  is  zero  so  that,  in  a 
Y-connected  alternator,  no  third  harmonic,  nor  any  harmonic 
which  is  a  multiple  of  three,  is  found  in  the  terminal  voltage 
wave. 

When  the  phases  are  A  -connected,  any  harmonic  in  the  voltage 
wave  of  one  phase  will  also  be  found  in  that  of  the  terminal  volt- 
age; a  greater  objection  to  the  use  of  this  connection  for  alterna- 
tors is  that  the  harmonics  cause  circulating  currents  to  flow  in  the 
closed  circuit  produced  by  the  A -connection.  Diagram  C 
shows  the  voltage  vector  diagram  for  the  fundamentals  in  the 
e.m.f.  wave  of  each  phase;  the  three  vectors  are  120  degrees  out  of 
phase  with  one  another  and  the  resultant  voltage  in  the  closed 
circuit  due  to  the  fundamentals  is  zero. 

Diagram  D  shows  the  voltage  vector  diagram  for  the  third 
harmonic  in  the  e.m.f.  wave  of  each  phase,  the  three  vectors 
are  360  -degrees  out  of  phase  with  one  another  and  the  resultant 
voltage  in  the  closed  circuit  due  to  the  third  harmonics  is  three 
times  the  value  of  the  third  harmonic  in  one  phase.  A  circulat- 
ing current  will  flow  in  the  closed  circuit,  of  triple  frequency  and 

<zj7 

of  a  value  =-=— -,  where  E3  is  the  effective  value  of  the  third 
<3z3 

harmonic  in  each  phase  and  23  is  the  impedence  per  phase  to  the 
third  harmonic. 

144.  Harmonics  Produced  by  Armature  Slots. — Fig.  133  shows 
two  positions  of  the  pole  of  an  alternator  relative  to  the  armature. 
In  position  A  the  air  gap  reluctance  is  a  minimum  and  in  position 
B  is  a  maximum.  The  flux  per  pole  pulsates,  due  to  this  change 
in  reluctance,  once  in  the  distance  of  a  slot-pitch,  or  2  a  times  in 
the  distance  of  two  pole-pitches,  where  a  =  slots  per  pole,  and  the 
e.m.f.  generated  in  each  coil  by  the  main  field  goes  through 
one  cycle  while  the  pole  moves,  relative  to  the  armature,  through 
the  distance  of  two  pole-pitches,  therefore  the  frequency  of  the 
flux  pulsation  —  2  a/. 

The  flux  per  pole  then  consists  of  a  constant  value  (f>a,  and  a 
superimposed  alternating  flux  which  has  a  frequency  of  2a 
times  the  fundamental  frequency  of  the  machine,  or  at  any 
instant  the  flux  per  pole 


THE  GENERATED  ELECTRO-MOTIVE  FORCE    185 


i  cos  2a6 

where  (f>a+4>i  is  the  maximum  value  of  the  pulsating  flux  and 
6  is  the  angle  moved  through  from  position  A,  Fig.  133,  in  elec- 
trical degrees;  therefore  the  flux  threading  coil  C}  which  is  a 
full-pitch  coil, 

^^a  +0i  when  the  coil  is  in  position  A 
=  [0a  +  0i  cos  2a#]cos  0  when  the  coil  has  moved  through 

6  electric  degrees  relative  to  the 
pole, 
and  the  e.m.f.  in  coil  C  at  any  instant 


B 


FIG.  133.  —  Variation  of  the  air  gap  reluctance. 

0i  cos  2a0)cps0 
~~ 


i  cos  2a6)cos9     dO 


27r/[-sin  0(^+^008  2ad}-cosd(2a^)1  sin  2aO}]T 
sin  6  +  ^sm  0  cos  2a6  +  2a<f)1  cos  d  sin  2a6]T 


sn 


-  (sin  (2a 


(sin 


(2a  - 


so  that,  due  to  the  variation  01  the  air  gap  reluctance  as  the  poles 
move  past  the  armature  slots,  two  harmonics  are  produced  which 
have  frequencies  of  (2a  +  l)  and  of  (2a  —  1)  times  that  of  the 
fundamental  respectively. 


186 


ELECTRICAL  MACHINE  DESIGN 


A  convenient  physical  interpretation  of  the  above  result  is 
as  follows:  A  and  B,  Fig.  134,  are  two  equal  trains  of  waves 
which  are  constant  in  magnitude,  and  move  in  opposite  directions 
at  the  same  speed.  The  resultant  of  two  such  wave  trains 
superimposed  on  one  another  is  a  series  of  stationary  waves  as 
shown  at  C. 

A  stationary  wave  such  as  that  of  the  alternating  magnetic 
field  in  the  air  gap  of  an  alternator  due  to  a  variation  in  the 
air  gap  reluctance,  can  therefore  be  exactly  represented  by  two 


FIG.  134. — Resolution  of   a  stationary  wave  into  two  progressive   waves. 

progressive  waves  of  constant  value  which  move  in  opposite 
directions  through  the  distance  of  two  pole-pitches  while  the 
alternating  wave  goes  through  one  cycle. 

Consider  both  of  these  waves  or  fields  to  exist  separately 
from  the  main  field  then,  when  the  pole  moves  with  the 
constant  flux  (f>a,  through  a  distance  y  relative  to  the  armature, 
one  of  these  constant  progressive  fields  moves  through  a  distance 
2ay  relative  to  the  pole,  or  through  a  distance  (2a  +  l)y 
relative  to  the  armature,  while  the  other  moves  through  a  dis- 
tance —  2  ay  relative  to  the  poles,  or  through  a  distance—  (2a—  l)y 


THE  GENERATED  ELECTRO-MOTIVE  FORCE    187 

relative  to  the  armature.  If  then  the  fundamental  frequency 
of  the  generated  e.m.f.  is  /,  the  two  other  fields  will  generate 
e.m.fs.  of  frequencies  =  (2a  +  I)/  and  (2a  —  I)/  respectively. 

To  keep  down  the  value  of  these  harmonics  the  reluctance  of 
the  air  gap  under  the  poles  should  be  made  as  nearly  constant 
as  possible  for  all  positions  of  the  pole  relative  to  the  armature. 

145.  Effect  of  the  Number  of  Slots  on  the  Terminal  E.M.F.— 
Fig.  135  shows  the  winding  diagrams  for  an  alternator  with 


A-  Three  Phase 


1       1       ' 

1       1       1 

A 

B 

III] 

^\                                                    , 

N^                                                                    * 

B-Two  Phase 

C-  Single  Phase 


A 

B 

C 

D 

\ 

D  -  Single  Phace 

FIG.  135.—  Effect  of  the  distribution  of  the  winding  on  the  terminal  voltage. 


six  slots  per  pole  and  wound  for  single,  two-  and  three-phase 
respectively,  the  same  punching  being  used  in  each  case.  The 
e.m.fs.  in  the  conductors  in  adjacent  slots  are  out  of  phase  with 

180 
one  another  by  the  angle  corresponding  to  one  slot-pitch  —  —^- 

=  30  electrical  degrees. 

In  the  three-phase  winding  the  conductors  in  slots  A  and  B 
are  connected  in  series  so  that  their  voltages  act  in  the  same 
direction;  the  resultant  voltage  Er,  diagram  E}  is  not  equal  to 


188  ELECTRICAL  MACHINE  DESIGN 

2e,  where  e  is  the  voltage  per  conductor,  but  is  the  resultant 
of  two  e.m.fs.  e  which  are  30  degrees  out  of  phase  with  one 
another  and  =  2e  X  0.96. 

In  the  case  of  the  two-phase  winding  the  conductors  A,  B  and 
C  are  connected  so  that  their  voltages  add  up  and  the  resultant 
voltage  Er  =  3e  X  0.91. 

In  the  case  of  the  single-phase  winding  where  all  the  con- 
ductors are  used  the  resultant  voltage  Er  =  $e  X  0.64,  while  if 
only  four  of  the  six  slots  per  pole  are  used,  as  shown  in  diagram 
D,  the  resultant  voltage  Er  =  4e  X  0.84,  which  is  only  10  per 
cent,  lower  than  that  obtained  when  all  six  slots  are  used.  A 
gain  of  10  per  cent,  in  voltage  is  not  worth  the  cost  of  the  50  per 
cent,  increase  in  armature  copper  that  is  required,  so  that  single- 
phase  machines  are  generally  wound  as  shown  in  diagram  D. 

146.  Rating  of  Alternators. — The  maximum  voltage  that  an 
alternator  can  give  continuously  is  limited  by  the  permissible 
value  of  the  flux  per  pole,  and  the  maximum  current  is  limited  by 
the  armature  copper  loss  which,  along  with  the  core  loss,  heats 
the  machine.     When  the  value  of  volts  and  amperes  is  fixed,  the 
kilowatt  rating  depends  only  on  the  power  factor  of  the  load. 
The  rpower  factor  is  a  variable  quantity,  and  one  over  which  the 
builder  of  the  machine  has  no  control,  so  that  an  alternator  is 
generally  rated  by  giving  the  product  of  volts  and  amperes, 
which  is  called  the  volt  ampere  rating,  and  this  quantity  divided 
by  1000  gives  the  rating  in  k.v.a.  (kilovolt  amperes). 

147.  Effect  of  the  Number  of  Phases  on  the  Rating. — Consider 
the  four  machines  whose  winding  diagrams  are  shown  in  Fig.  135, 
and  let  the  number  of  conductors  per  slot  be  the  same  in  each, 
then  the  voltage  per  phase  is  given  in  the  following  table : 

Number  of  phases  Voltage  per  phase 

Single-phase  (all  slots  used)  constant  X  6e  X  0.64. 

Single-phase  (2/3  of  slots  used)  constant  X4e  X0.84. 

Two-phase  constant  X  3e  X0.91. 

Three-phase  constant  X  2e  X0.96. 

Since  there  are  the  same  number  of  conductors  per  slot* 
these  conductors  have  the  same  section  and  therefore  carry  the 
same  current  Ic;  the  volt  ampere  rating,  which  equals  volts  per 
phase  X  current  per  phase  X  number  of  phases,  is  given  in  the 
following  table: 


THE  GENERATED  ELECTRO-MOTIVE  FORCE    189 

Number  of  phases  Volt  ampere  rating 

Single-phase  (all  slots  used)  constant  X  6e  X  0.64  X  1 X  /c. 

Single-phase  (2/3  of  slots  used)  constant  X4eX0.84X  lX/c- 

Two-phase  constant  X3eX0.9lX2X/c. 

Three-phase  constant  X 2eX 0.96X3 X/r. 

=  a  constant  X  0.64. 

=  a  constant  X0.56. 

=  a  constant  X0.91. 

=  a  constant  X  0.96. 

In  practice  the  machine  is  given  the  same  rating  for  both 
two-  and  three-phase  windings,  although  the  three-phase  machine 
is  the  better,  and  is  given  65  per  cent,  of  this  rating  when 
wound  for  single-phase  operation. 

148.  The  General  E.M.F.  Equation.— It  is  shown  in  Art.  145 
that,    when   the   winding    of    an  alternator  is  distributed,  the 
terminal  voltage  is  less  than  ZXe 
where  Z  =  conductors  in  series  per  phase 

e  =  volts  per  conductor 

and  is  equal  to  kZe  where  k  is  the  distribution  factor  and  is 
found  from  the  following  table,  which  is  worked  up  by  the 
method  explained  in  Art.  145: 

Slots  per  phase  Distribution  factor 

per  pole  Two-phase  Three-phase 

1  1.0  1.0 

2  0.924  ,0.966 

3  0.911  0.96 

4  0.906  0.958 
6  0.903  0.956 

The  single  phase  results  are  not  tabulated  since  they  depend  on 
the  number  of  slots  that  are  used  by  the  winding. 

When  a  short-pitch  is  used,  as  is  often  done  with  double  layer 
windings,  then,  as  shown  in  Fig.  136,  which  shows  part  of  a  three- 
phase  double  layer  winding  with  three  slots  per  phase  per  pole, 
the  two  adjacent  belts  A  and  B  are  out  of  phase  with  one 
another  by  6  degrees,  and,  as  shown  in  Fig.  137,  the  resultant 

voltage,  when  these  two  belts  are  put  in  series,  is  equal  to  twice 

f\ 

the  voltage  in  one  belt  multiplied  by  cos  ^. 

It  was  shown  in  Art.  137  that  the  effective  e.m.f.  per  con- 
ductor =  2.22  (f>af  10~8  volts. 


190 


ELECTRICAL  MACHINE  DESIGN 


If  the  winding  is  full-pitch  and  is  not  distributed  then  the 
voltage  per  phase  =  2.22  Z  <paf  10~8  volts. 


FIG.  136. — Short-pitch  winding. 

If  the  winding  is  full-pitch  and  is  distributed,   the  voltage 
per  phase 

-8  (25) 


FIG.  137.  —  Vector  diagram  for  a  short-pitch  winding. 

and  finally,  if  the  winding  is  short-pitch,  so  that  the  winding 
belts  are  out  of  phase  with  one  another  by  6  degrees,  and  is 
also  distributed,  then  the  voltage  per  phase 


=  2.22  kZ(/>aflQ-8  cos 


(26) 


CHAPTER  XIX 
CONSTRUCTION  OF  ALTERNATORS 

Figure  138  shows  the  type  of  construction  that  is  generally 
used  for  alternators;  it  is  known  as  the  revolving  field  type. 

149.  The  Stator. — In  the  revolving  field  type  of  machine  the 
stator  is  the  armature.  B,  the  stator  core,  is  built  up  of  lamina- 


FIG.  138. — Revolving  field  alternator. 

tions  of  sheet  steel  0.014  in.  thick,  which  are  insulated  from  one 
another  by  layers  of  varnish  and  are  then  mounted  in  a  self- 
supporting  cast-iron  yoke  A.  These  laminations  are  punched 
on  the  inner  periphery  with  slots  C  which  carry  the  stator  coils 
D.  The  type  of  slot  shown  is  the  open  slot;  it  has  the  advan- 
tage over  the  closed  slot  that  the  coils  can  be  fully  insulated  be- 

191 


192 


ELECTRICAL  MACHINE  DESIGN 


fore  being  put  into  the  machine  and  can  also  be  more  easily 
repaired. 

The  stator  core  is  divided  into  blocks  by  means  of  vent  seg- 
ments of  cast  brass,  and  the  duels  thereby  provided  allow  air 
to  circulate  freely  through  the  machine  to  keep  it  cool.  The 
vent  ducts  are  spaced  about  3  in.  apart  and  are  half  an  inch 
wide. 

The  stator  laminations  and  vent  segments  are  clamped 
between  two  cast-steel  end  heads  E.  When  the  teeth  are  long 
they  are  supported  by  strong  finger  supports  placed  at  F}  be- 
tween the  end  heads  and  the  end  punchings  of  the  core. 


FIG.  139.— Poles  and  field  coil. 

When  the  external  diameter  of  the  stator  core  is  less  than 
30  in.  the  core  punching  is  generally  made  in  a  complete  ring; 
when  this  diameter  is  greater  than  30  in.  the  core  is  generally 
built  up  in  segments  which,  as  shown  in  Fig.  138,  are  fixed  to  the 
yoke  by  means  of  dovetails;  the  segments  of  adjacent  layers  of 
laminations  break  joint  with  one  another  so  as  to  overlap  and 
produce  a  solid  core. 

150.  Poles  and  Field  Ring. — Inside  of  the  stator  revolves  the 
rotor  or  revolving  field  system.  The  poles  G  carry  the  exciting 


CONSTRUCTION  OF  ALTERNATORS 


193 


coils  H  and  are  excited  by  direct  current  from  some  external 
source.  0 

The  excitation  voltage  is  independent  of  the  terminal  voltage 
of  the  machine  and  is  generally  chosen  low,  so  that  for  a  given 
excitation  the  field  current  will  be  comparatively  large  and  the 
field  coils  will  have  few  turns. 

For  the  usual  excitation  voltage  of  120  it  will  generally  be 
possible,  except  on  the  smaller  machines,  to  use  the  type  of  field 
winding  shown  in  Fig.  139,  which  is  made  by  bending  strip  copper 
on  edge;  the  layers  of  strip  copper  are  insulated  from  one  another 
by  layers  of  paper  about  0.01  in.  thick,  and  the  whole  field  coil  is 
supported  by  and  insulated  from  the  poles  and  field  ring  as  shown 
at  A,  Fig.  140.  For  small  machines  the  excitation  loss  is  com- 


3  Turns  0.015 
Paper. 


X'"Brass  Collar. 

^"Fiber  Collar,      .  ,, 

3  Turns  O.Ol&Taper. 

M"Fiber  Collar. 


FIG.  140. — Alternator  field  coils. 

paratively  low,  and  with  an  excitation  voltage  of  120  the  section 
of  the  wire  is  too  small  and  the  number  of  turns  required  too  large 
to  allow  the  use  of  a  strip  copper  coil;  in  such  cases  double  cotton- 
covered  square  wire  is  used  as  shown  at  B,  Fig.  140;  the  coils  are 
tapered  so  as  to  allow  free  circulation  of  air  around  them. 

Since  the  number  of  poles  in  an  alternator  is  fixed  by  the  speed 
and  the  frequency,  it  rarely  happens  that  this  number  is  such  as 
to  allow  the  use  of  a  pole  of  circular  section;  the  pole  is  generally 
rectangular  in  section  and,  as  shown  in  Fig.  139,  is  built  up  of 
punchings  of  sheet  steel  0.025  in.  thick  which  are  riveted  together 
between  two  cast-steel  end  plates. 

The  poles  are  generally  attached  to  the  field  ring  by  means  of 
bolts  as  shown  at  K,  Fig.  138,  or  by  means  of  dovetails  and 
tapered  keys  as  shown  at  L;  two  tapered  keys  are  used  which 
are  driven  in  from  opposite  ends. 

13 


194 


ELECTRICAL  MACHINE  DESIGN 


The  exciting  current  is  led  into  the  revolving  field  system  by 
means  of  brushes  which  bear  on  cast-iron  or  cast-bras^  slip  rings; 
the  slip  rings  are  carried  by  and  insulated  from  the  shaft  as 
shown  at  M;  the  brushes  are  generally  of  soft  self -lubricating 
carbon  and  carry  about  75  amperes  per  square  inch. 


FIG.  141. — Revolving  field  alternator. 

The  stator  of  an  alternator  is  seldom  split  except  in  the  case 
of  very  large  machines  where  it  is  done  for  convenience  in  ship- 
ment. In  order  that  the  stator  windings  can  be  examined  and 
easily  repaired  it  is  advisable  to  arrange  that  the  whole  stator 
slide  axially  on  the  base,  and  the  key  shown  at  N  is  for  the  pur- 
pose of  keeping  the  alignment  correct. 

Fig.  141  shows  a  1000-k.v.a.  water-wheel  driven  alternator  of 
the  type  described  in  this  chapter. 


CHAPTER  XX 
INSULATION 

The  insulation  of  low-voltage  machines  has  been  discussed 
in  Chapter  IV  and  presents  no  particular  difficulty,  since  insu- 
lation which  is  strong  enough  mechanically  is  generally  ample  for 
electrical  purppses  up  to  600  volts.  For  higher  voltages,  how- 
ever, the  thickness  of  insulation  required  to  prevent  breakdown 
is  great  compared  with  that  required  for  mechanical  strength  and, 
unless  such  insulation  is  carefully  designed,  trouble  is  liable  to 
develop. 

151.    Definitions. — If    a    difference    of    electric    potential    be 


A 
FIG.  142. — Distribution  of  the  dielectric  flux. 

established  between  two  electrodes  a  and  6,  Fig.  142,  which  are 
separated  by  an  insulating  material  or  dielectric,  a  molecular 
strain  will  be  set  up  in  the  dielectric. 

This  molecular  strain  is  conveniently  represented  by  lines  of 
dielectric  flux,  and  the  number  of  lines  per  unit  area,  which  is 
called  the  Dielectric  Flux  Density,  is  taken  as  a  measure  of  the 
strain. 

When  the  dielectric  flux  density  reaches  a  certain  critical  value 

195 


196 


ELECTRICAL  MACHINE  DESIGN 


the  material  is  disrupted  and  loses  its  insulating  properties; 
this  critical  value  depends  on  the  nature,  thickness  and  condition 
of  the  material. 

The  distribution  of  dielectric  flux  depends  largely  on  the  shape 
of  the  electrodes,  as  shown  in  diagrams  A  and  B,  Fig.  142.  When 
an  insulating  material  of  uniform  thickness  t  is  placed  between 
two  parallel  plates  and  subjected  to  a  voltage  E}  the  dielectric 
flux  density  or  molecular  strain  is  uniform  through  the  total 
thickness  of  the  material  and  is  conveniently  represented  by  the 

E 

ratio  —>  the  volts  per  unit  thickness,     Under  such  conditions  of 
t 

test,  the  highest  effective  alternating  voltage  that  }  mil  (0.001  in.) 
thickness  of  the  material  will  withstand  for  1  minute  is  generally 
called  its  Dielectric  Strength. 


FIG.  143. — Potential  gradient  at  a  slot  corner. 
When  the  dielectric  flux  density  is  not  uniform  throughout 

Tfl 

the  total  thickness  of  the  material,  the  ratio-,-,  the  volts    per 

L 

unit  thickness,  has  little  meaning.  In  Fig.  143  for  example, 
which  shows  the  dielectric  flux  distribution  at  the  corner  of  a 
slot,  it  will  be  seen  that  the  dielectric  flux  density,  or  molecular 
strain,  is  greatest  at  the  surface  of  the  conductor  and  decreases 
as  the  lines  spread  out.  Under  such  conditions  the  strain  at  any 
point  is  conveniently  expressed  by  what  is  known  as  the  Potential 
Gradient  at  the  point,  where  this  quantity  is  the  volts  per  unit 
thickness  that  would  be  required  to  set  up  the  same  dielectric 


INSULATION 


197 


flux  density  as  that  at  the  point  in  question  if  the  material  were 
of  uniform  thickness  and  tested  between  two  parallel  plates. 
The  potential  gradient  across  ab  is  given  by  curve  A. 

152.  Insulators  in  Series. — If  an  air  film  be  placed  between 
two  electrodes  and  subjected  to  a  difference  of  potential,  a  certain 
dielectric  flux  density  will  be  produced  in  the  air.  If  now  the  air 
be  replaced  by  mica,  a  greater  dielectric  flux  density  will  be 
produced  for  the  same  difference  of  potential.  The  Specific 
Inductive  Capacity  of  an  insulating  material  is  defined  as 
the  dielectric  flux  density  in  the  material 

the  dielectric  flux  density  in  air 
for  the  same  value  of  volts  per  mil. 

Figure  144  shows  two  cases  of  dielectric  subjected  to  a  difference 
of  electric  potential  between  electrodes  of  the  same  size  and  the 
same  distance  apart.  In  A  the  dielectric  is  air,  and  in  B  is 
made  up  of  air  and  mica  in  series.  Since  the  specific  inductive 
capacity  of  mica  is  greater  than  that  of  the  air  which  it  replaces, 


FIG.  144. — Effect  of  the  specific  inductive  capacity  of  the  dielectric  on 
the  dielectric  flux  density. 


being  about  6,  the  dielectric  flux  density  is  greater  in  B  than 
in  A  for  the  same  difference  of  potential  between  the  electrodes, 
and  the  air  in  B  is  subjected  to  a  greater  strain  than  that  in 
A,  so  that  it  will  break  down  at  a  lower  value  of  voltage  between 
the  terminals,  although  at  the  same  value  of  volts  per  mil. 

Since  in  B  the  two  materials,  air  and  mica,  are  in  series,  the 
dielectric  flux  density  is  the  same  in  each  and  therefore,  from 
the  definition  of  specific  inductive-  capacity, 
the  volts  per  mil  thickness  in  the  mica_  1 

the  volts  per  mil  thickness  in  the  air     ~sp.  ind.  cap  of  mica 

=  -  approximately 

The  greater  the  thickness  of  mica  in  the  total  thickness  be- 
tween electrodes  the  larger  will  be  the  dielectric  flux  density 


198  ELECTRICAL  MACHINE  DESIGN 

and  the  greater  therefore  the  value  of  volts  per  mil  thickness  in  the 
air  for  a  given  voltage  between  the  electrodes. 

153.  Effect   of  Air  Films   in   Insulation. — From    the    above 
discussion  it  will  be  seen  that,  should  there  be  an  air  film  in  the 
thickness  of  a  solid  dielectric,  then,  for  a  perfectly  conservative 
value  of  volts  per  mil  of  total  thickness  of  the  dielectric,  the 
volts  per  mil  across  the  air  film  may  be  sufficient  to  disrupt  it  if 
the  solid  dielectric  have  a  specific  inductive  capacity  greater 
than  one. 

When  air  is  disrupted  ozone  and  oxides  of  nitrogen  are  formed, 
these  oxidize  nearly-  all  the  insulators  used  for  electrical  ma- 
chinery except  mica  and  thereby  seriously  impair  their  in- 
sulating properties. 

154.  The  Design  of  Insulation. — The  voltage  that   a   given 
insulation  will  stand  depends  on 


FIG.  145. — Effect  of  the  voltage  on  the  thickness  of  the  slot  insulation. 

The  thickness  of  the  insulation; 
The  dielectric  strength  of  the  material; 
The  potential  gradient  across  the  material; 
The  length  of  time  that  the  voltage  is  applied. 

155.  The  Thickness  of  the  Insulation. — Fig.   145  shows  the 
slot  of  an  alternator  insulated  in  the  one  case  for  high  voltage 
and  in  the  other  case  for  low  voltage.     If  the  space  occupied  by 
insulation  could  be  filled  with  copper  the  output  of  the  machine 
could  be  considerably  increased,  so  that  the  solution  of  high 
voltage    insulation    problems    is   not    solved    economically  by 
indefinitely    increasing    the    thickness    of    the    dielectric    with 
increasing  voltage,  but  by  the  selection  and  proper  use  of  the 
most  suitable  materials. 

156.  The  Potential  Gradient. — Insulating  materials  break  down 
wherever  they  are  overstressed,  and  if  the  stress  is  not  uniform 


INSULATION 


199 


they  break  down  first  at  the  point  of  highest  stress;  it  is  therefore 
necessary  to  make  a  study  of  the  distribution  of  stress,  or  of  the 
potential  gradient  in  the  material. 

Consider  the  case  of  the  slot  corner  shown  in  Fig.  143,  the 
lines  of  dielectric^  flux  pass  radially  from  the  conductor  to  the 
side  of  the  slot,  so  that  the  dielectric  flux  density  is  a  maximum 
at  the  surface  of  the  conductor  and  a  minimum  at  the  surface  of 
the  slot  and  the  potential  gradient  curve,  if  the  dielectric  is 
of  the  same  material  throughout,  is  as  shown  in  diagram  A. 
The  inner  layers  of  the  insulation  therefore  carry  more  than 
their  share  of  the  voltage,  and  these  layers  break  down  long 
before  the  stress  in  the  outer  layers  reaches  the  break- 
down point. 


FIG.  146. — Potential  gradient  with  graded  insulation. 

It  is  possible  to  make  the  outer  layers  carry  their  share  of  the 
total  voltage  by  grading  the  insulation  in  the  following  way: 
Materials  having  different  specific  inductive  capacities  are  used 
and  put  on  in  layers  in  such  a  way  that  the  lower  the  specific 
inductive  capacity  the  further  away  is  the  material  from  the 
conductor.  This  relieves  the  strain  on  the  inner  layers  because, 
as  pointed  out  in  the  discussion  of  insulators  in  series,  the  voltage 
required  to  send  a  given  dielectric  flux  through  a  layer  of  insulat- 
ing material  is  inversely  as  the  specific  inductive  capacity  of  the 
material,  so  that  the  higher  the  specific  inductive  capacity  of  the 
inner  layers  the  lower  the  voltage  drop  across  these  layers  and 
the  higher  therefore  the  voltage  drop  across  the  outer  layers. 


200 


ELECTRICAL  MACHINE  DESIGN 


The  potential  gradient  for  such  insulation,  made  up  in  three 
layers,  is  shown  in  diagram  J5,  Fig.  146. 

The  potential  gradient  can  be  controlled  in  many  cases  by  a 
slight  alteration  in  the  shape  of  the  surfaces  to  be  insulated  from 
one  another.  Fig.  147  shows  three  cases  of  slot  insulation,  and  it 
is  evident  that  the  potential  gradient  is  more  uniform  in  case  B 
than  in  case  A,  while  case  C  is  the  best  of  the  three  because  of  the 
extra  thickness  of  the  dielectric  at  the  corner;  in  this  last  case 
the  insulation  generally  punctures  between  the  parallel  sides  of 


FIG.  147. — Effect  of  the  shape  of  the  surfaces  to  be  insulated  on  the 
distribution  of  dielectric  flux. 

the  slot  and  conductor,  and  not  at  the  corner.  Since  the  stress 
is  uniform  through  the  thickness  of  the  insulation  when  it  is 
between  two  parallel  surfaces,  grading  of  the  insulation  has  no 
advantages  for  machines  whose  slots  have  square  corners. 

157.  Time  of  Application  of  Electric  Strain.1— That  the  voltage 
at  which  an  insulating  material  will  puncture  depends  on  the 


Time 


FIG.  148. — Effect  of  time  on  the  puncture  voltage. 

length  of  time  that  this  voltage  is  applied  is  shown  by  the  curve 
in  Fig.  148.  E  is  the  maximum  voltage  that  the  material  will 
withstand  for  an  infinite  length  of  time  without  deterioration 
due  to  heating  and  consequent  puncture. 

If  air  films  are  present  in  the  insulation  then  a  lower  voltage 
than  E  will  cause  puncture  if  applied  for  some  time,  but  the  action 
in  this  case  is  a  secondary  one. 

Fleming  and  Johnson,  Journal  of  the  Institution  of  Elect.  Eng.,  Vol.  47, 
page  530. 


INSULATION  201 

In  Art.  152,  page  197,  it  was  pointed  out  that  the  stress  on  an 
air  film  bedded  in  a  material  of  specific  inductive  capacity  greater 
than  one  is  very  high,  and  that  the  film  may  become  ruptured 
and  ozone  and  oxides  of  nitrogen  be  produced  which  attack 
the  other  insulation  causing  deterioration  and  consequent 
puncture. 

The  amount  of  these  gases  produced  by  the  rupture  of  a  thin 
air  film  is  not  enough  to  do  much  harm  unless  there  is  a  constant 
supply  of  air  to  the  film.  When  an  electrical  machine  is  started 
up  its  coils  become  heated  and,  since  the  gases  in  the  film  expand, 
some  of  them  are  expelled.  When  the  machine  is  shut  down  the 
coils  cool  off,  the  gases  in  the  film  contract,  and  a  fresh  supply  of 
air  is  drawn  in.  This  action  is  known  as  the  breathing  action 
of  the  coils. 

Trouble  due  to  this  breathing  action  takes  months  to  develop 
and  usually  shows  up  as  a  breakdown  between  adjacent  turns; 
the  insulation  between  these  turns  having  become  brittle  due  to 
oxidization,  readily  pulverizes  due  to  vibration.  The  trouble  can 
be  eliminated  by  constructing  the  coils  so  that  they  contain  no 
air  pockets,  and  in  the  endeavor  to  do  this  various  methods  have 
been  adopted  for  impregnating  the  coils  and  sealing  their  ends. 
The  compounds  generally  used  for  impregnating  purposes  are 
made  fluid  by  heating  to  a  temperature  of  about  100°  C.,  and  in 
cooling  to  normal  temperatures  most  of  them  contract  about  10 
per  cent,  and  this  10  per  cent,  becomes  filled  with  air. 

Since,  with  the  present  methods  of  insulating,  it  may  be  con- 
sidered impossible  to  eliminate  all  the  air  pockets  from  a  coil,  it 
is  necessary  to  keep  the  stress  in  the  air  films  below  that  value  at 
which  they  will  rupture.  This  can  be  done  by  increasing  the 
total  thickness  of  the  insulation  and  also  by  the  use  of  material 
which  has  a  low  specific  inductive  capacity.  It  is  unfortunate 
that  mica,  which  is  one  of  the  most  reliable  of  insulators,  has  a 
high  specific  inductive  capacity;  a  good  composite  insulator  can  be 
made  up  of  mica  paper,  which  consists  of  a  layer  of  mica  backed  by 
a  layer  of  paper;  the  specific  inductive  capacity  of  the  former  is 
about  six,  and  of  the  latter  is  about  two,  while  the  combination 
has  a  value  between  these  two  figures. 

Such  an  insulation  is  described  fully  on  page  205  and  may  be 
expected  to  withstand  45  volts  per  mil  indefinitely  without 
trouble  due  to  the  breakdown  of  air  films.  For  such  insulation 
then  the  minimum  thickness  in  mils  between  the  conductor  and 


202 


ELECTRICAL  MACHINE  DESIGN 


the  side  of    the  slot  = 


volts  from  cond.  to  ground 
45 


If    the   in- 


sulation were  made  up  entirely  of  mica  a  greater  total  thickness 
would  be  required  on  account  of  the  high  specific  inductive 
capacity  of  the  mica,  while  if  made  up  entirely  of  paper  a  smaller 
total  thickness  would  be  required  so  far  as  the  breakdown  of  the 
air  film  is  concerned,  but  paper  is  not  reliable  as  an  insulator 
when  used  alone. 

158.  Design  of  Slot  Insulation. — The  following  points  are 
taken  up  fully  in  Chapter  IV: — 

The  materials  in  general  use  are;  micanite  and  empire  cloth, 
which  are  used  principally  on  account  of  their  dielectric  strength; 


ooo 


OOP 
000 

OOP 
©Q© 

©@® 


oo© 
o®@ 
o@© 

00® 

oo© 
oo© 


A  B 

FIG.  149. — Insulation  between  layers  of  conductors. 

tape,  which  is  used  principally  to  bind  the  conductors  together; 
paper,  which  is  used  to  protect  the  other  insulation. 

The  puncture  test  recommended  by  the  American  Institute 
of  Electrical  Engineers  is  given  in  the  table  on  page  34. 

The  end  connections  should  be  insulated  for  the  full  voltage 
between  the  terminals. 

To  minimize  surface  leakage  the  slot  insulation  should  be 
carried  beyond  the  core  for  a  distance  which  depends  on  the 
voltage  and  which  is  found  from  the  table  on  page  35. 

159.  Insulation  between  Conductors  in  the  Same  Slot. — In 
high-voltage  alternators  the  number  of  turns  per  coil  is  large 
and  the  size  of  the  wire  comparatively  small.  Fig.  149  shows 
sections  through  two  alternator  slots;  in  A  the  winding  is  double 
layer  and  in  B  is  chain;  the  conductors  are  numbered  in  the 
order  in  which  they  are  wound. 


INSULATION 


203 


Between  conductors  1  and  2,  2  and  3,  3  and  4,  etc.,  there 
is  the  voltage  of  only  one  turn  or  of  two  conductors,  be- 
tween 2  and  5  there  is  the  voltage  of  six  conductors  and 
between  1  and  6  the  voltage  of  ten  conductors.  These  con- 
ductors are  usually  of  double  cotton-covered  wire,  and  it  has 
been  found  advisable  to  increase  this  insulation,  by  putting  in 
layers  of  empire  cloth  as  shown,  when  the  voltage  between 
adjacent  conductors  exceeds  25  volts,  because  the  impregnation 
of  the  cotton  may  not  be  thorough,  and  the  cotton  covering 
may  become  damaged  when  the  conductors  are  squeezed 
together. 

160.  Examples  of  Alternator  and  Induction  Motor  Insulation. — 

Example  i. — Insulation  for  a  440- volt  induction  motor  with  a  wire- wound 
coil  and  a  double  layer  winding. 

A  section  through  the  slot  and  insulation  is  shown  in  Fig.  150,  and  the 
insulation  consists  of: 

(a)  Double  cotton  covering  on  the  conductors. 

(b)  A  layer  of  empire  cloth  0.006  in.  thick  between  horizontal  layers  of 
conductors. 

(c)  One  turn  of  paper  0.01  in.  thick  on  the  slot  part  of  the  coil  to  hold  the 
conductors  in  layers. 

(d)  One  layer  of  half-lapped  empire  cloth  tape  0.006  in.  thick  all  round 
the  coil. 

(e)  One  turn  of  paper  0.01  in.  thick  on  the  slot  part  of  the  coil  to  protect 
the  empire  cloth. 

(f)  One  layer  of  half-lapped  cotton  tape  0.006  in.  thick  on  the  end  con- 
nections to  protect  the  empire  cloth. 

The  coil  is  baked  and  impregnated  before  the  paper  and  cotton 
tape  are  put  on,  and  is  dipped  in  finishing  varnish  after  they  are 
put  on  to  make  it  water-  and  oil-proof. 

The  thickness  of  the  slot  insulation  and  the  apparent  dielec- 
tric strength  are  given  in  the  table  below: 


Width 

Depth 

Voltage 

D   C   C  on  wire53 

600 

Paper  
Empire  cloth                                    •  . 

0.02 

o  024 

0.03 
0.024 

2,500 
4,500 

Paper             

0.02 

0.03 

2,500 

0.064 

0.084 

10,100 

204 


ELECTRICAL  MACHINE  DESIGN 


In  the  above  table,  under  heading  of  width,  is  given  the  space 
taken  up  in  the  width  of  the  slot  by  the  different  layers  of 
insulation.  The  insulation  on  the  conductors  has  not  been 
added  since  it  varies  with  the  number  of  conductors  per  slot. 

Under  the  heading  of  depth  is  .given  the  space  taken  up  in  the 
depth  of  half  a  slot  by  the  different  layers  of  insulation. 

Under  the  heading  of  voltage  is  given  the  apparent  dielectric 
strength  of  the  insulation;  the  figures  used  for  the  different 
materials  are  taken  from  Chapter  IV. 

The  puncture  test  voltage  is  2000;  therefore  the  factor  of 
safety  is  5.0. 


FIG.  150.— 440  volt 
slot  insulation. 


FIG.  151.— 2200  volt 
slot  insulation. 


Example  2. — Insulation  for  a  2200-volt  induction  motor  with  a  strip 
copper  coil  and  a  double-layer  winding. 

A  section  through  the  slot  and  insulation  is  shown  in  Fig.  151  and  the 
insulation  consists  of: 

(a)  One  layer  of  half-lapped  cotton  tape  0.006   in.  thick  on  each   con- 
ductor to  form  the  insulation  between  conductors. 

(b)  One  layer  of  half -lapped  cotton  tape  0.006  in.  thick  all  round  the 
coil  to  bind  the  conductors  together. 

(c)  One  turn  of  micanite  0.02  in.  thick  on  the  slot  part  of  the  coil. 

(d)  Two  layers  of  half-lapped  empire  cloth  0.006  in.  thick  all  round  the 
coil. 

(e)  One  turn  of  paper  0.01  in.  thick  on  the  slot  part  of  the  coil  to  protect 
the  empire  cloth. 

(f)  One  layer  of  half-lapped  cotton  tape  0.006  in.  thick  on  the  end  con- 
nections to  protect  the  empire  cloth. 


INSULATION 


205 


The  coil  is  baked  and  impregnated  before  the  paper  and  last 
taping  of  cotton  tape  are  put  on.  After  they  are  on,  the  slot 
part  of  the  coil  is  hot  pressed  and  then  allowed  to  cool  under  pres- 
sure, after  which  the  coil  is  dipped  in  finishing  varnish  to  make 
it  water-  and  oil-proof. 

The  thickness  of  the  insulation  and  the  apparent  dielectric 
strength  are  given  in  the  table  below. 


Width 

Depth 

Voltage 

Tape  on  conductor 

1  000 

Tape  on  coil  
Micanite  
Empire  cloth 

0.024 
0.04 
0  048 

0.024 
0.06 
0  048 

1,000 
16,000 
9  000 

Paper  

0.02 

0.03* 

2,500 

0.132 

0.162 

29,500 

The  puncture  test  voltage  is  5000;  therefore  the  factor  of 
safety  is  5.8. 

Example  3. — Insulation  for  a  11, 000- volt  alternator  with  a  strip  copper 
coil  and  a  chain  winding. 

A  section  through  the  slot  and  insulation  is  shown  in  Fig.  152  and  the 
insulation  consists  of  : 

(a)  One  layer  of  half-lapped  cotton  tape  0.006  in.  thick  on  each  con- 
ductor to  form  the  insulation  between  adjacent  conductors. 

(b)  One  layer  of  micanite  0.02  in.  thick  between  vertical  layers  of  con- 
ductors, all  round  the  coil. 

(c)  Two  layers  of  half-lapped  empire  cloth  0.006  in.  thick  on  each  of  the 
two  sections  of  the  coil,  this  empire  cloth  to  go  on  both  slot  part  and  end 
connections  of  the  coil. 

(d)  One  layer  of  cotton  tape  0.006  in.  thick,  half-lapped  on  the  ends  and 
taped  with  a  butt  joint  on  the  slot  part  of  the  coil.     This  tape  is  to  bind 
the  two  sections  of  the  coil  firmly  together. 

(e)  Three  turns  of  mica  paper,  made  of  5  mil  paper  and  7  mil  mica,  on  the 
slot  part  of  the  coil. 

(f)  One  layer  of  cotton  tape  0.006  in.  thick,  half  lapped  on  the  ends  and 
butt  joint  on  the  slot  part  of  the  coil. 

(g)  Bake  and  impregnate  the  coil. 

(h)  Three  layers  of  half-lapped  empire  cloth  0.006  in.  thick  all  round  the 
coil. 

(j)  Three  turns  of  mica  paper  on  the  slot  part  of  the  coil. 

(k)  One  layer  of  cotton  tape  0.006  in.  thick,  half-lapped  on  the  ends  and 
butt  joint  on  the  slot  part  of  the  coil. 


206 


ELECTRICAL  MACHINE  DESIGN 


(1)  Two  layers  of  half-lapped  empire  cloth  0.006  in.  thick  all  round  the  coil. 

(m)  Three  turns  of  mica  paper  on  the  slot  part  of  the  coil. 

(n)  Three  layers  of  half-lapped  empire  cloth  0.006  in.  thick  all  round  the 
coil. 

(o)  One  layer  of  cotton  tape  0.006  in.  thick,  half -lapped  on  the  ends  and 
butt  joint  on  the  slot  part  of  the  coil. 

(p)   Bake  and  impregnate  the  coil. 

(q)  One  turn  of  paper  0.015  in.  thick  on  the  slot  part  of  the  coil. 

(r)  Hot  press  the  slot  part  of  the  coil  and  allow  it  to  cool  while  under 
pressure. 


FIG.  152. — 11,000  volt  slot  insulation. 

The  thickness  of   the  insulation  and  its  apparent  dielectric 
strength  are  given  in  the  table  below. 


Width 

Depth 

Voltage 

(a)     Tape  on  conductor 

1  000 

(b)    Micanite  between  layers  
(c)     Empire  cloth  on  each  section  . 
(d)    Cotton  tape              

0.02 

0.096 
0  012 

0.048 
0.012 

9,000 

(e)     Mica  paper  

0.084 

0.072 

20,550 

(f  )     Cotton  tape  
(h)     Empire  cloth 

0.012 
0  072 

0.012 
0  072 

13  500 

(j)  •   Mica  paper  
(k)    Cotton  tape 

0.084 
0  012 

0.072 
0  012 

20,550 

(1)      Empire  cloth  
(m)  Mica  paper  
(n)    Empire  clotji 

0.048 
0.084 
0  072 

0.048 
0.072 
0  072 

9,000 
20,550 
13,500 

(o)    Cotton  tape  

0.012 

0.012 

(q)    Paper  

0.045 

0.045 

3,750 

0.653 

0.549 

111,400 

INSULATION  207 

The   minimum  thickness   of  insulation  between  copper  and 
iron  =  279  mils,  therefore  the  volts  per  mil  at  normal  voltage  =40. 

The  puncture  test  voltage  for  this  insulation  is  22;000  volts, 
therefore  the  factor  of  safety  is  5.1. 

The  insulation  on  each  end  connection  consists  of: 
10  layers  of  half-lapped  empire  cloth 
5  layers  of  half -lapped  cotton  tape; 
this  insulation,  along  with  the  air  space  between  coils,  is  ample. 


CHAPTER  XXI 

ARMATURE  REACTIONS  IN  ALTERNATORS 
POLYPHASE  MACHINES 

161.  The  Armature  Fields. — a  and  6,  Fig.  153,  are  two  con- 
ductors of  one  phase  of  a  polyphase  alternator.     When  current 
flows  in  these  conductors  they  become  encircled  by  lines  of  force. 
These  lines  may  be  divided  into  two  groups;  <f>r,  the  lines  which 
pass  through  the  magnetic  circuit  and  whose  effect  is  called 
armature  reaction,  and  (/>x  ,  called  leakage  lines,  which  do  not  pass 
through  the  magnetic  circuit. 

162.  Armature  Reaction. — Diagram  A,  Fig.  154,  shows  an  end 
view  of  part  of  a  three-phase  alternator  which  has  six  slots  per 
pole.     The  starts  of  the  three  windings  are  spaced  120  electrical 


FIG.  153. — The  armature  fields. 

degrees  apart  and  are  marked  £u  $2,  £3.  The  armature  moves 
relative  to  the  poles  in  the  direction  of  the  arrow  and  the  e.m.f .  in 
each  phase  at  any  instant  is  given  by  the  curves  in  diagram  F. 
In  diagram  A  is  shown  the  relative  position  of  the  armature  and 
poles,  and  also  the  direction  of  the  e.m.f.  in  each  conductor,  at 
instant  1,  diagram  F,  at  which  instant  the  e.m.f.  in  phase  1  is 
a  maximum. 

Let  the  current  be  in  phase  with  the  generated  e.m.f.,  then 
diagram  G  shows  the  current  in  each  phase  at  any  instant,  and 
the  three  diagrams,  B,  C  and  D,  show  the  direction  of  the  current 
in  each  conductor  and  also  the  relative  position  of  the  poles  and 
armature  at  the  three  instants  1,  2  and  3.  It  may  be  seen  from 
these  diagrams  that  the  currents  in  the  three  phases  produce  a 
resultant  armature  m.m.f.  which  moves  in  the  same  direction  as 
the  poles  and  at  the  same  speed.  Since  the  armature  resultant 

208 


ARMATURE  REACTIONS  IN  ALTERNATORS     209 


m.m.f .  is  added  to  that  of  the  main  field  at  one  pole  tip,  and  sub- 
tracted from  it  at  the  other  tip  of  the  same  pole,  the  resultant 
effect  is  cross-magnetizing. 

Let  the  current  lag  the  generated  e.m.f.  by  90  degrees,  then 
diagram  H  shows  the  current  in  each  phase  at  any  instant,  and 


Ph.l 


Ph.2        Ph.3 


(oWT)   (*)  ©   £>)  ®   O 


N  S  N 

Direction  of  Generated  E.M.F. 


\/ 


Ph.3 


Armature  M.M.F.  when  Current 
is  in  Phase  with  Generated  E.M.F. 


=  0 

-0.86  JTO 
=  0.86/m 


\ 


A 


Ph.1       Ph.2 


Armature  M.M.F.  when  Current 
TLags  the  Generated  E.M.F.  by  90  Degrees. 


FIG.  154. — The  armature  m.m.f.  of  a  three  phase  alternator. 

diagram  E  shows  the  direction  of  the  current  in  each  conductor 
and  also  the  relative  position  of  the  poles  and  armature  at  instant 
1.  The  resultant  m.m.f.  of  the  armature  has  the  same  value  as 
before  and  moves  at  the  same  speed  and  in  the  same  direction,  but 
has  now  a  different  position  relative  to  the  poles  and  is  demag- 
netizing in  effect. 

14 


210  ELECTRICAL  MACHINE  DESIGN 

If  the  current  lead  the  generated  e.m.f.  by  90  degrees;  then  it 
can  be  shown  in  a  similar  way  that  the  resultant  armature  m.m.f. 
has  the  same  magnitude,  speed  and  direction  as  before,  but  is 
magnetizing  in  effect. 

163.  The  Alternator  Vector  Diagram. — On  no-load  the  current 
in  the  windings  of  an  alternator  is  zero  and  the  only  m.m.f.  which 
is  acting  across  the  air  gap  is  F0,  that  due  to  the  main  field;  FQ 
sends  a  constant  flux  cf>a  across  the  gap.  This  flux  moves  rela- 
tive to  the  armature  surface  so  that  the  flux  which,  due  to  the 
m.m.f.  F0,  threads  the  windings  of  one  phase  of  the  armature  is 
alternating  and  has  a  maximum  value  =  (j>a. 

The  voltage  generated  in  a  coil  lags  the  flux  which  threads  the 
coil,  and  whose  change  produces  the  voltage,  by  90  degrees;  thus, 
in  Fig.  155,  the  flux  threading  coil  a  is  a  maximum  but  the  voltage 

a  b  a  b 

O ® O ® 


FIG.  155. — The  generated  e.m.f.  in  a  coil. 

in  that  coil  is  zero,  while  the  total  flux  threading  the  coil  6  is  zero 
and  the  voltage  in  that  coil  is  a  maximum;  that  is,  the  voltage  is 
in  phase  with  the  flux  which  the  coil  cuts,  but  lags  the  flux  which 
threads  the  coil  by  90  degrees. 

The  vector  diagram  for  one  phase  of  a  polyphase  alternator  is 
shown  in  Fig.  156.  On  no-load,  F0f  the  m.m.f.  of  the  main 
field  referred  to  the  armature,  produces  an  alternating  flux  in 
the  windings  of  each  phase,  and  E0,  the  voltage  generated  in 
each  phase  by  that  flux,  lags  FQ  by  90  degrees. 

When  the  alternator  is  loaded  the  currents  in  the  armature 
produce  a  m.m.f.  Fa  of  armature  reaction  which,  if  acting  alone, 
produces  a  field  (j)r  of  constant  strength  which  moves  in  the 
same  direction  and  at  the  same  speed  as  the  main  field. 

In  Fig.  154,  diagram  B,  it  may  be  seen  that  when  the  current 
in  phase  1  is  a  maximum  the  flux  which  threads  the  windings  of 
that  phase  is  also  a  maximum;  in  diagram  C  the  current  in  phase 
2  is  zero  and  the  flux  which  threads  the  windings  of  that  phase 
is  also  zero.  In  general  it  may  be  shown  that  the  flux  which,  due 
to  the  revolving  field  (f>r,  threads  the  winding  of  one  phase  of 
the  armature  is  an  alternating  flux  which  has  a  maximum  value 
=  <f>r  and  is  in  phase  with  the  current  in  that  winding. 


ARMATURE  REACTIONS  IN  ALTERNATORS     211 


If  the  alternator  is  loaded  and  I,  Fig.  156,  is  the  current  per 
phase,  then  Fg,  the  resultant  of  the  m.m.fs.  .F0  and  Fa,  will 
produce  a  resultant  magnetic  flux  <j>a  which  is  alternating  with 
respect  to  the  armature  windings,  and  Eg,  the  voltage  per  phase 
due  to  the  flux  <j>g,  will  lag  it  by  90  degrees. 

In  addition  to  the  m.m.f.  of  armature  reaction  the  current  in 
the  windings  of  one  phase  sets  up  an  alternating  magnetic  flux 
cf)x  which,  as  shown  in  Fig.  153,  circles  these  windings  but  does 
not  link  the  magnetic  circuit;  this  flux  is  in  phase  with  the 
current  in  the  windings  and  is  proportional  to  that  current  since 
its  magnetic  circuit  is  not  saturated  at  normal  tooth  densities. 


FIG.  156. — The  vector  diagram  for  an  alternator. 

In  Fig.  156  F0  is  the  m.m.f.  due  to  the  field  excitation  referred 
to  one  phase  of  the  armature. 
E0     is  the  voltage  per  phase  which  would  be  generated  by  the 

flux  produced  by  F0. 
I       is  the  current  per  phase. 
Fa    is    the    m.m.f.    of     armature     reaction     referred    to     one 

phase  of  the  armature  and,  as  pointed  out  above,  is  in  phase 

with  /. 

Fg     is  the  resultant  of  the  two  m.m.fs.  F0  and  Fa. 
(f>g    is  the  flux  that  threads  the  windings  of  one  phase  due  to  Fg. 
Eg     is  the  voltage  generated  in  that  phase  by  (f>g. 
(f)x    is  the    armature  leakage  flux   per  phase  produced  by  7. 
Ex    is  the  voltage  per  phase  generated  by  the  flux  <f>x    and  is 

called  the  leakage  reactance  voltage. 

EX=IX  where    X  is    the    leakage    reactance    per    phase. 


E 
Et 


is  the  resultant  of  Eg  and  E3 


is  the  terminal  voltage  per  phase  and   =   E-IR  taken  as 
vectors,  where   R  is   the    effective    resistance    per   phase. 


212 


ELECTRICAL  MACHINE  DESIGN 


Figure  157  shows  the  above  diagram  for  the  particular  case 
where  the  power  factor  is  approximately  zero  and  the  current 
lags  the  generated  voltage  by  90  degrees.  In  this  case  the 
m.m.f.  of  armature  reaction  is  subtracted  directly  from  that  of 


FIG.  157. — The  vector  diagram  for  an  alternator  on  zero  power  factor. 

the  main  field  to  give  the  resultant  m.m.f.,  and  the  leakage 
reactance  voltage  is  subtracted  directly  from  the  generated 
voltage  Eg  to  give  the  terminal  voltage.  The  resistance  drop 


O          Ampere  Turns  per  Pole         9 

FIG.  153. — The  saturation  curves  of  an  alternator. 

can  be  neglected  in  this  case  since  its  phase  relation  is  such  that 
it  has  little  effect  on  the  value  of  the  terminal  voltage. 

164.  Full -load  Saturation  Curve  at  Zero  Power  Factor  with 
Lagging  Current. — Curve  1,  Fig.  158,  shows  the  no-load  satura- 


ARMATURE  REACTIONS  IN  ALTERNATORS     213 

tion  curve  of  an  alternator.  When  the  machine  is  loaded,  the 
power  factor  of  the  load  zero,  and  the  current  lagging,  the  m.m.f. 
of  armature  reaction  is  directly  demagnetizing,  and  to  overcome 
its  effect  and  maintain  the  flux  <£>a  which  crosses  the  air  gap 
constant,  a  number  of  ampere-turns  per  pole  equal  to  the  arma- 
ture demagnetizing  ampere-turns  per  pole  must  be  added  to  the 
main  field  excitation.  Under  these  conditions  the  increase  in  the 
field  excitation  causes  the  leakage  flux  (j>e,  Fig.  159,  to  increase 
to  the  value.  0/e,  where 

A  T.g+t  +  demagnetizing  AT.  per  pole\ 


without  increasing  the  value  of  <j)a,  the  flux  crossing  the  air  gap. 


The  leakage  factor  at    no-load  = 


^ 


while   that   for   the 


above  load  conditions  =• 


«*— 

>^ 

1 

h-J 

f 

\ 

[-«.- 

- 

FIG.  159. — The  main  field  and  the  pole  leakage. 

Curve  2,  Fig.  158,  is  a  new  no-load  saturation  curve  which  is 
calculated  with  the  value  of  the  leakage  factor  corresponding 
to  full-load,  zero  power  factor  and  lagging  current. 

To  maintain  the  flux  crossing  the  air  gap  constant  and  =  <f>a 
a  number  of  ampere- turns  per  pole,  ab,  equal  to  the  armature 
demagnetizing  ampere-turns  per  pole,  must  be  added  to  the 
value  obtained  from  curve  2. 

The  terminal  voltage  is  less  than  that  generated  due  to  the  flux 
<j)a  by  IX,  the  leakage  reactance  voltage;  the  resistance  drop 
being  neglected  on  zero  power  factor  since,  as  shown  in  Fig. 
157,  its  phase  relation  is  such  that  it  has  little  effect  on  the 
terminal  voltage. 

The  locus  of  point  c  so  found  is  the  full-load  saturation  curve  at 
zero  power  factor  with  lagging  current. 

|  165.  Synchronous  Reactance. — In  Fig.  158,  de,  the  drop  in 
voltage  due  to  the  increase  in  leakage  factor,  depends  on  the 
demagnetizing  effect  of  the  armature,  which  is  proportional  to 


214 


ELECTRICAL  MACHINE  DESIGN 


the  current  and,  as  shown  in  Fig.  154,  varies  with  the  power 
factor,  being  zero  for  unity  power  factor  and  a  maximum  for 
zero  power  factor  lagging;  this  drop  may,  therefore,  be  considered 
as  part  of  that  due  to  armature  reaction.  In  Fig.  158,  then, 
the  total  voltage  drop  is  made  up  of  two  parts  one,  db,  due  to 
armature  reaction,  which  varies  with  the  slope  of  curve  1  and 
therefore  with  the  excitation,  and  the  other,  be,  the  armature 
reactance  drop,  which  is  practically  constant  for  all  excitations. 

Since,  for  a  given  excitation,  each  of  these  voltage  drops  is 
proportional  to  the  current  and  since,  as  shown  in  Fig.  156,  they 
are  always  in  phase  with  one  another,  their  sum,  namely  dc, 
Fig.  158  or  E0E,  Fig.  156,  may  be  represented  by  a  fictitious 
reactance  voltage  called  the  synchronous  reactance  voltage  and 
=  IX,  where  X  is  the  synchronous  reactance  per  phase.  It 
may  be  seen  from  Fig.  158  that  dc,  and  therefore  X,  is  not 
constant  but  decreases  as  the  field  excitation  and,  theretore,  the 
saturation  of  the  magnetic  circuit  increases. 

166.  The  Demagnetizing  Ampere -turns  per  Pole  at  Zero 
Power  Factor. — The  distribution  of  the  m.m.f.  of  armature 


267, 


r 


6=Cond.  per  Slot 


_©_ 


3.61 
0.6  T 
-r — 


A  B 

FIG.  160. — Armature  m.m.f.  on  zero  power  factor. 

reaction  at  two  different  instants  is  shown  in  Fig.  160  for  a 
machine  with  six  slots  per  pole  and  b  conductors  per  slot.  These 
diagrams  are  taken  directly  from  Fig.  154,  and  the  relative  posi- 
tion of  poles  and  armature  shown  is  that  corresponding  to  zero 
power  factor  and  lagging  current. 

The  portion  of  this  m.m.f.  which  is  effective  in  demagnetizing 
the  poles  is  shown  cross  hatched,  it  is  required  to  find  ATaV)  the 
average  value  of  this  cross  hatched  part  of  the  curve,  for  the  case 
where  c/»  =  0.6  and  therefore  the  pole  covers  3.6  slots. 


ARMATURE  REACTIONS  IN  ALTERNATORS    215 


=  area  of  cross  hatched  curve,  diagram  A 
=  2  6/m;  +  1.5  67 


=  area  of  cross  hatched  curve,  diagram  B 

=  1.73  &7WX3;.+0.866  6/mX0.6^ 

=  5.7  blml 

=  5.656/m^;  an  average  value  from  diagrams  A 

and  B 
therefore  ATav  =  1.57  blm 

=  2.22  blc  where  Ic  is  the  effective  current 
per  pole  ' 


=  2.22  Me  x 


per  pole 

=  0.37Xcond.  per  poleX/c.  (27) 

It  the  pole  enclosure  be  increased  to  0.7  the  value  of  ATav  will 
be  reduced  to  0.33Xcond.  per  poleX/c- 

The  value  can  be  found  in  a  similar  way  to  the  above  for  any 
particular  value  of  pole  enclosure,  number  of  phases  and  slots 
per  pole,  but  the  value  of  ATav  is  generally  taken  as0.35Xcond. 
per  pole  X  Ic  for  all  polyphase  machines. 

cfo  y6xc  Cond. 


\ 


FIG.  161. — The  armature  leakage  fields  with  a  chain  winding. 

167.  Calculation  of  the  Leakage  Reactance. — Fig.  161  shows 
part  of  the  winding  of  one  phase  of  a  polyphase  alternator 
which  has  a  chain  winding. 

If  <j>e  =  the  lines  of   force   that  circle  1  in.   length   of   the  belt 
of  end  connections  for  each  ampere  conductor  in  that  belt, 


216  ELECTRICAL  MACHINE  DESIGN 

<j)s  =  the  lines  of  force  that  cross  the  slots  and  circle  1  in.  length 
of  the  phase  belt  of  conductors  for  each  ampere  conductor 
in  that  belt, 

</>j=the  lines  of  force  that  cross  the  tooth  tips  and  circle  1  in. 
length  of  the  phase  belt  of  conductors  for  each   ampere 
conductor  in  that  belt, 
6  =  conductors  per  slot, 
c  =  slots  per  phase  per  pole, 

then  the  total  flux  that  links  the  coils  shown 


the  coefficient  of  self-induction  of  these  coils 

= : — —  1 0  ~8  henry 

i 

=  b2c2  [0eX2Le  +  (0s  +(f)t)  X2Lc]XlO~8  henry 
the  reactance  of  these  coils  in  ohms 

-  2nfb2c2[<t>e  X  2Le  +  (0.  +  00  X  2LC]  X  10~8 

since  there  are  p/2  of  these   groups  of   coils  per  phase 
the  reactance  of  one  phase  in  ohms 

=  2;r/p62c2[0eLe  +  (0.  +  00  X  Lc]  X 10"8  (28) 

For  a  double  layer  winding  a  slight  modification  is  required 
in  the  above  formula. 

Figure  162  shows  part  of  the  winding  of  one  phase  of  a  poly- 
phase alternator  which  has  a  double  layer  winding. 

be 
The  number  of  turns  in  the  coils  shown  =-=- 

the  total  flux  that  links  these  coils 

=  0C 

.  bXc 


the  coefficient  of  self-induction  of  these  coils 
henry 

-*   henry 


ARMATURE  REACTIONS  IN  ALTERNATORS     217 
the  reactance  of  these  coils  in  ohms 


since  there  are  p  of  these  groups  of  coils  per  phase, 
the  reactance  of  one  phase 


(29) 


which  differs  from  the  formula  for  the  chain  winding  in  that 
the  end  connection  reactance  is  reduced  to  half  the  value. 


V2  b  c  Cond. 


FIG.  162. — The  armature  leakage  fields  with  a  double  layer  winding. 
168.  End -connection  Reactance.— 0e  depends  principally  on 


20 


16 


12 


8       12       16       20       24      28 
Pole  Pitch  in  Inches 


FIG.  163. — The  end  connection  leakage  flux. 

the   length   of  the  end-connection  leakage  path,  namely,  the 
length  around  the  belt  of  end  connections,  which,  as  may  be  seen 


218 


ELECTRICAL  MACHINE  DESIGN 


from  Figs.  161  and  162,  is  directly  proportional  to  the  pole-pitch 
and  inversely  proportional  to  the   number  of  the  phases,  and 

(f>e  decreases  as  this  length  increases,  so  that  —  is    approxi- 

TL 

i 


mately  proportional  to 


for  any  number  of  phases. 


pole  pitch 

Le,  the  length  of  the  end  connections,  increases  with  the  pole- 
pitch  as  may  be  seen  from  Figs.  161  and  162,  and  in  Fig.  163 

-   is   plotted   against  pole-pitch  from  test  results. 

^,  **-  -e^         ,/ 


m 


d, 


FIG.  164.  —  The  slot  leakage  flux. 

169.  Slot  Reactance.  —  Fig.   164  shows  part  of  one    phase   of 
an  alternator  which  has  a  chain  winding.     The  m.m.f.  between 

m  and  n  =  b  X  cXi  X^r  ampere-turns,  therefore  the    leakage 
a  -t 

flux  d(j> 

2.5±  all  in  inch  units 


cs 


the  reluctance  of  the  iron  part  of  the  leakage  path  is  neglected 
since  it  is  small  compared  with  that  of  the  air  path  across  the 
slots. 


ARMATURE  REACTIONS  IN  ALTERNATORS     219 

This  flux  d<j)  links  each  side  of  the  be  jr  turns  of  the  coils  shown 

al 

and  the  interlinkages  per  unit  current 


The  coefficient  of  self-induction  of  the  coils  shown,  due  to  the 
flux  which  crosses  the  slots,  between  the  limits  y  =  o  and  y  =  dl 


henry 


cXs  6 

The  m.m.f.   between  e    and  /,  Fig.   164,  =cbi  ampere-turns, 
therefore  the  leakage  flux  crossing  the  slots  above  the  conductors 


cw 

the  coefficient  of  self-induction  of   the  coils  shown  due  to  this 
flux 

=  3.2c262X2Lc  fa+-?$L-+*±)  10~8  henry 

cs     cs  +  w      cw 


therefore  the  total  coefficient  of  self-induction  of  the  coils  shown 
due  to  the  total  slot  leakage 

=  3.2c62X2Lc  (^+-2  +  ^4+^)  10-8  henry 
3s      s       s  +  w      w 


and  the  slot  reactance  of  these  coils  in  ohms 


4     lO" 

w 


since  there  are  p/2  of  these  groups  of  coils  per  phase  the  slot 
reactance  per  phase 


220 


ELECTRICAL  MACHINE  DESIGN 


^  io-« 


S  +  W       W 


where 


2d, 


3s     s     s+w 

170.  Tooth -tip  Reactance. — A,  Fig.  165,  shows  the  tooth-tip 
leakage  path  round  one  side  of  the  coils  of  one  phase  of  a  machine 
which  has  1  slot  per  phase  per  pole,  when  the  winding  of  that 
phase  lies  between  the  poles. 


dy 

f 


ff^L 


\ 


h1  n 


FIG.  165.— Tooth-tip  leakage  flux. 


The  m.m.f.  between  e  and/  =bci  ampere-turns 
therefore  the  leakage  flux  d(j>  per  1  in.  length  of  core 
4:7i          dy 

=  10^- 


X2.54  all  in  inch  units 


dy 


and  the  total  tooth-tip  leakage  flux  that  links  one  phase  belt 
per  1  in.  length  of  core 


f 

=  3.26ci    I 
Jo 


dy 


ARMATURE  REACTIONS  IN  ALTERNATORS    221 

- 2.35  to  log,.  (l+ 1) 

therefore  <j>ta,  the  lines  of  force  that  cross  the  tooth  tips  and 
circle  1  in.  length  of  the  phase  belt  of  conductors  for  each  ampere 
conductor  in  that  belt,  when  the  belt  lies  between  the  poles, 


B  shows  the  case  where  there  are  two  slots  per  phase  per  pole 
and  it  may  be  seen  that  in  such  a  case 


. 


-2.JWJ  log, 


C  shows  the  case  where  there  are  three  slots  per  phase  per  pole 
and  it  may  be  seen  that  in  such  a  case 

the  flux  2.35  Iogl0  1  1  +—  *       1  circles  the  total  belt 

while  the  flux       —  Iog10  (  1  H  —  (is  produced  by,  and  circles  1  /3  of 
6  \       w/ 

the  total  belt. 

This  latter  flux  is  equivalent  to  a  flux  -^—  log  10(  1  +—  )    circling 

y  \      w/ 

the  whole  belt, 

+  + 


therefore  fc.  -  2.35  logl  +3  +          log,,    l  + 

D  shows  the  tooth-tip  leakage  path  round  the  coils  of  one 
phase  of  a  machine  with  1  slot  per  phase  per  pole,  when  the 
winding  of  that  phase  lies  under  the  poles.  In  this  case  <j)tp, 
the  lines  of  force  that  cross  the  tooth  tips  and  circle  1  in.  length 
of  the  phase  belt  of  conductors  for  each  ampere  conductor  in 
that  belt,  when  the  belt  lies  under  the  poles, 

-32^ 
6-Z  2d 

In  the  case  where  there  are  two  slots  per  phase  per  pole  as 
shown  in  E 


222 


ELECTRICAL  MACHINE  DESIGN 


In  the  case  where  there  are  three  slots  per  phase  per  pole  as 
shown  in  F 

IXC     3.2     txC 


In  Fig.  166  the  tooth-tip  flux  per  ampere  conductor  per  inch 
is  approximately 

=  (f>ta  while  the  conductors  are  in  the  belt  hk 
=  <j>tp  while  the  conductors  are  in  the  belt  kl 


FIG.  166. — Variation  of  the  current  in  the  phase  belt  at  zero  power  factor 
with  the  position  of  the  belt  relative  to  the  poles. 


On  zero  power  factor  the  current  in  a  conductor  is  a  maximum 
when  the  e.m.f.  generated  in  that  conductor  is  zero,  that  is 
when  the  conductor  is  between  the  poles.  As  the  conductor  moves 
relative  to  the  poles  the  current  in  the  conductor  varies  accord- 
ing to  a  sine  law  as  shown  in  Fig.  166,  therefore,  since  the  tooth- 
tip  reactance  per  phase 

=  27ifb2c2p<f>taLc^O~8  when  the  cond.  are  in  the  belt  hk 
and  =  27r/62c2p</>ipLc10~8  when  the  cond.  are  in  the  belt  kl 
the  effective  voltage  per  phase  on  zero  power  factor  due  to  tooth- 
tip  leakage 

=  27r/62c2p<^aLc10~8X  effective    current   between    h    and   k, 

while  they  are  in  this  belt 

and  =2nfb2c2p(j>tpLclO~sX effective    current   between   k   and   I, 

while  they  are  in  this  latter  belt 


ARMATURE  REACTIONS  IN  ALTERNATORS    223 

and  from  formula  28,  page  216,  the  effective  voltage  per  phase 
due  to  tooth-tip  leakage 


therefore  </>,  is  approximately 

./i=# 

"  \     1 


1  —  <      effect,  current  in  belt  hk 


effect,  current  in  belt  kl 


As  a  general  rule,  (ft,  the  pole  enclosure  =  0.6 
and  for  this  value  1  —  <p  =  0.4 

effective  current  m  cond.  in  belt  hk        =0.93  Imax 
effective  current  in  cond.  in  belt  kl        =0.5  Imax 


therefore  0,  =  0,ax0.4  x-5^  +  &„  X0.6x 


171  Final  Reactance  Formula.  —  The  reactance  of  one  phase 
of  a  polyphase  machine  with  a  pole  enclosure  of  approximately 
60  per  cent,  is 


c)10-8  28 

for  chain  windings 


]  Lc)  10-8  29 


for  double  layer  windings 
where  </>eLe  may  be  found  from  Fig.  163 

=  ^/^     d        2d^     d4 
c      3s      s      s  +  w     w 


>fa  =  2.35   Iog10  (  1  -\  —  J  for  1  slot  per  phase  per  pole 


=  2.35  Iog10  (  1  +-^—r-. )  for  2  slots  per  phase  per  pole 

- 


for  3  slots  per  phase  per  pole 


224  ELECTRICAL  MACHINE  DESIGN 

txC 


for  1  or  2  slots  per  phase  per  pole 


10 

=  3.2  XTT  X^  —  -s  for  3  slots  per  phase  per  pole 


f=  frequency  in  cycles  per  second 
6  =  cond.  per  slot 
c  =  slots  per  phase  per  pole 
p  =  poles 
n  =  phases 

Lc  =  frame  length  in  inches 
t  =  width  of  tooth  at  the  tip 

C  =  Carter  coefficient  found  from  Fig.  40,  page  44. 
slot  dimensions  are  given  in  Figs.  164  and  165. 

Example  of  Calculation.  —  The  armature  reaction  and  armature 
reactance  can  be  checked  approximately  by  the  no-load  satura- 
tion and  the  short-circuit  curves  of  an  alternator.  Fig.  167 
shows  the  actual  test  curves  on  a  small  alternator  which  was 
built  as  follows: 

Poles,  6 

Pole  enclosure,  0  .  6 

Pole  pitch,  10.5  in. 

Air  gap  clearance,         0.2  in. 
Slots  per  pole,  6 

Conductors  per  slot,      12 
Size  of  slot,  0  .  75  X  1  .  75  in.  ,  open 

Tooth  width,  1  .  0  in. 

Carter  coefficient,          1  .  2 
Frame  length,  6.5  in. 

Winding,  double  layer 

Y-connected 

Turns  per  field  coil,      420 
Rating,  65  k.v.a.,  600  volts,  three-phase,  60  cycles. 

To  send  full-load  current  through  the  machine  on  short-circuit 
requires  an  excitation  of  4.8  amperes.  Now  the  power  factor 
during  this  test  is  zero  since  the  machine  is  carrying  no-load,  and 
the  terminal  voltage  is  zero  since  the  machine  is  short-circuited, 
therefore  m  is-  a  point  on  the  full-load  saturation  curve  at  zero 
power  factor,  the  resistance  drop  being  neglected. 
The  demagnetizing  ampere-turns  per  pole 

=  0.35Xcond.  per  poleX/c 

-0.35X12X6X62.5 

=  1580  ampere-turns  per  pole 
the  corresponding  field  current 


ARMATURE  REACTIONS  IN  ALTERNATORS     225 
_  demagnetizing  ampere- turns  per  pole 


field-turns  per  pole 
1580 

420 
=  3.75 

700 
600 

500 
§400 

•g 

etf 

Jsoo 

200 
100 

0 

amperes 

§  | 

Armature  Current 

, 

^ 

X 

•T 

1  * 

*y 

/ 

/ 

// 

' 

1 

/ 

/ 

/ 

& 

• 

/ 

S 

-/  4 

V 

/  J 

°5 

/ 

4 

4 

<• 

y 

Full 

Load 

Curre 

Qt 

b 

/    ! 

// 

n4  m-             8                   12                  16                  20 
Field  Current 

FIG.    167.  —  No-load  saturation  and  short  circuit   curves   on  a,   65   k.v.a 
three-phase  alternator. 


The  reactance  per  phase 


c     10-8ohms. 


where  — ~  =  5Xn  from  Fig.  163,  since  the  pole-pitch  =10.5  in. 

=  15 
3.2/    1.5         .25 


=2.35  log  (l+^Xl      )  .0.82 


15 


226 


ELECTRICAL  MACHINE  DESIGN 


4>t    =0.52X0.82+0.42X9.6=4.4 
and  reactance  per  phase 

=  2 X?r X60 X122X22X 6(15. +  (1.6 +4.4)6.5)  X10~8 
=  0.7  ohms. 

The  voltage  drop  per  phase  =  0.7X62. 5  =  44  volts 
and  the  voltage  drop  at  the  terminals    =1.73x44 

=  76  volts 

since  the  winding  is  Y-connected. 
These  two  figures,  3.75  field  amperes 

76  terminal  volts 

are  the  only  ones  required  for  the  construction  of  triangle  abm, 
Fig.  167,  and  it  may  be  seen  that  the  calculated  results  check 
the  test  results  very  closely. 

172.  Variation  of  Armature  Reaction  and  Armature  Reactance 
with  Power  Factor. — When  an  alternator  is  carrying  a  load 
whose  power  factor  is  zero,  the  current  in  the  conductors  reaches 


<n 


r 


A  5 

Current  lags  by  90  degrees.  Current  is  in  phase. 

FIG.  168. — Effect  on  the  armature  reaction  of  the  phase  relation  between 
the  current  and  the  generated  e.m.f. 

a  maximum  when  the  conductors  are  between  the  poles;  the 
tooth-tip  leakage  is  then  a  minimum.  When,  however,  the  cur- 
rent is  in  phase  with  the  generated  voltage,  it  reaches  a  maxi- 
mum when  the  conductors  are  under  the  center  of  the  poles;  the 
tooth-tip  leakage  is  then  a  maximum.  The  voltage  drop  due  to 
armature  reactance,  therefore,  varies  with  the  power  factor  and 
is  a  maximum  when  the  current  is  in  phase  with  the  generated 
voltage  and  a  minimum  when  the  current  is  out  of  phase  with 
that  voltage  by  90  degrees. 


ARMATURE  REACTIONS  IN  ALTERNATORS    227 

The  distribution  of  the  m.m.f.  of  armature  reaction  lor  the 
same  two  cases  is  shown  in  Fig.  168;  diagram  A  shows  the  dis- 
tribution when  the  current  lags  the  generated  voltage  by  90 
degrees  and  the  armature  m.m.f.  is  demagnetizing;  diagram  B 
shows  the  distribution  when  the  current  is  in  phase  with  the  gen- 
erated voltage  and  the  armature  m.m.f.  is  cross  magnetizing.  It 
may  be  seen  from  these  diagrams  that  A  Tav,  the  average  value  of 
the  part  of  this  m.m.f.  which  is  effective,  is  a  minimum  when  the 
current  is  in  phase  with  the  generated  voltage  and  a  maximum 
when  the  current  is  out  of  phase  by  90  degrees. 

The  variation  of  armature  reactance  and  armature  reaction 
with  power  factor  is  difficult  to  calculate  and  it  is  usual  to 
assume  that  any  decrease  in  one  of  them  with  a  change  in 
power  factor  is  counterbalanced  by  an  increase  in  the  other 
so  that  the  resultant  effect,  which  is  represented  by  a  syn- 
chronous reactance,  is  constant  at  all  power  factors,  for  a 
given  field  excitation. 

173.  Full -Load  Saturation  Curve  at  Any  Power  Factor. — Given 
the  no-load  saturation  curve  and  also  that  at  full-load  and  zero 


FIG.  169. — Vector  diagram  for  an  alternator. 

power  factor,   it  is  required  to  draw  in  the  full-load  saturation 
curves  for  other  power  factors.     The  method  adopted  to  deter- 
mine different  points  on  these  curves  is  shown  in  Fig.  169,  where 
the  diagram  shown  by  heavy  lines  is  taken  from  Fig.  156. 
E0  =  the  no-load  voltage  per  phase  corresponding  to  the  field 

excitation  og,  Fig.  176,  page  237  and  =dg, 
E0E  =ihe  synchronous  reactance  drop  =  dc,  Fig.  176, 
EtE  =  ihe  resistance  drop  per  phase, 


228  ELECTRICAL  MACHINE  DESIGN 

0  =  the  phase  angle  between  Et  and  7, 
cos#  =  the  power  factor  of  the  load. 

The  construction  generally  adopted  to  find  Et  is  shown  by 
the  dotted  lines  in  Fig.  169. 

Triangle  acd  is  drawn  to  scale  in  the  proper  phase  relation  with 
/  and  equal  to  triangle  EE0Et. 

Line  am  is  set  off  at  an  angle  6  such  that  cos  6  is  the  power 
factor  at  which  it  is  desired  to  find  the  terminal  voltage. 

With  d  as  center  and  E0  as  radius  the  line  am  is  cut  at  Et  and 
the  value  Et  is  then  plotted  along  the  ordinate  of  field  excitation 
for  which  E0  is  the  no-load  voltage  and  ='gf,  Fig.  176,  for  85 
per  cent,  power  factor. 

174.  Regulation. — The  regulation  of  an  alternator  is  defined 
as  the  per  cent,  increase  in  voltage  when  full  load  is  thrown  off 
the  machine,  the  speed    and  excitation  being  kept   constant, 
and  is  equal  to 

r-'  Fig.  176,  at  unity  power  factor, 
00 

~i  Fig.  176,  at  85  per  cent,  power  factor, 

jy 

-rjj  Fig.  176,  at  zero  power  factor. 
kit 

175.  Effect  of  Pole  Saturation  on  the  Regulation. — A^  and  Blt 
Fig.  170,  are  the  no-load  saturation  curves  of  two  alternators 
which  have  armatures  that  are  exactly  alike;  the  field  systems 
differ  in  that  machine  A  has  a  smaller  air  gap  and  a  greater  pole 
density  than  has  machine  B\  the  excitation  is  the  same  for  each 
machine  at  normal  voltage  and  no-load. 

•  A2  and  B2  are  the  no-load  saturation  curves  with  the  full-load 
leakage  factor,  the  effect  of  the  increase  in  the  leakage  factor 
is  the  greater  in  the  machine  which  has  the  higher  pole  density. 

A  3  and  B3  are  the  full-load  saturation  curves  at  zero  power 
factor;  the  demagnetizing  ampere-turns  per  pole  are  the  same 
in  each  case;  the  armature  reactance  drop  is  slightly  greater  in 
the  machine  with  the  smaller  air  gap  clearance. 

It  may  be  seen  that  the  machine  with  the  saturated  poles  is 
that  -which  has  the  best  regulation;  but  it  is  also  the  machine 
which  takes  the  largest  field  excitation  on  load. 

Of  two  machines  that  are  built  to  meet  the  same  regulation 
guarantee,  that  with  the  higher  pole  density  is  generally  the 


ARMATURE  REACTIONS  IN  ALTERNATORS    229 


cheaper,  because,  as  shown  in  Fig.  170,  for  the  same  armature 
reaction  and  reactance  it  gives  the  better  regulation  or  for  the 
same  regulation  it  can  have  the  greater  armature  reaction  and 
reactance.  If  these  quantities  are  increased  by  increasing  the 
number  of  armature  turns  then,  for  constant  output,  the  flux 
per  pole  must  be  decreased  in  the  same  ratio  and  the  whole 
machine  may  be  made  smaller.  In  order  to  carry  an  increased 
number  of  conductors  on  a  smaller  diameter  it  is  necessary  to 
increase  the  slot  depth. 


Field  Ampere  Turns  per  Pole 
FIG.   170. — Effect  of  pole  saturation  on  the  regulation. 

The  pole  density  is  seldom  carried  above  95,000  lines  per 
square  inch  at  no-load  and  normal  voltage,  because  for  higher 
densities  it  is  difficult  to  predetermine  the  saturation  curves  with 
sufficient  accuracy  to  ensure  that  there  is  enough  field  excitation 
at  the  high  densities  corresponding  to  normal  voltage,  full-load 
and  zero  power  factor,  since  the  permeability  of  the  iron  used 
may  be  lower  than  was  expected. 

176. — Relation  between  the  M.M.Fs.  of  Field  and  Armature.— 
In  Fig.  171,  A1  and  B1  are  the  no-load  saturation  curves,  A2  and 
B2  the  no-load  saturation  curves  with  the  full-load  leakage 
factor,  As  and  B3  the  full-load  saturation  curves  at  zero  power 
factor,  of  two  machines  which  are  alike  in  every  respect  except 
that  the  air  gap  of  machine  A  is  smaller  than  that  of  machine  B. 

It  may  be  seen  from  these  curves  that,  the  larger  the  air  gap 


230 


ELECTRICAL  MACHINE  DESIGN 


and  therefore  the  larger  the  ratio  of 


field  AT.  per  pole 


the 


armature  AT.  per  pole' 
better  is  the  regulation,  and  that  the  armature  ampere-turns  per 
pole  must  be  a  small  fraction  of  the  field  ampere-turns  per  pole 
if  the  regulation  is  to  be  at  all  reasonable.  To  consider  an  extreme 
case,  suppose  that  the  demagnetizing  ampere-turns  per  pole 
at  full-load  were  equal  to  the  no-load  ampere-turns  on  the  field, 


0  Field  Ampere  Turns  per  Pole 

FIG.  171. — Effect  of  the  relative  strengths  of  the  field  and  armature  m.m.f's. 

on  the  regulation. 

then  on  zero  power  factor  with  full-load  current  the  armature 
field  would  wipe  out  the  main  field  and  the  terminal  voltage 
would  be  zero. 

In  practice,  the  maximum  field  ampere-turns  per  pole,  namely 
OZ,  Fig.  171,  is  generally  made  greater  than  three  times 
the  armature  ampere-turns  per  pole;  the  greater  this  ratio 
the  better  will  be  the  regulation  of  the  machine,  other  things 
being  unchanged,  but  the  greater  will  be  the  cost  of  the  field  copper 
required  and  the  greater  the  difficulty  in  cooling  the  field  coils. 

It  must  be  understood  that  the  regulation  of  an  alternator 
will  seldom  be  better  than  8  per  cent,  at  full-load  and  unity  power 
factor  and  18  per  cent,  at  full-load  and  85  per  cent,  power  factor 


ARMATURE  REACTIONS  IN  ALTERNATORS    231 


because  of  the  cost  of  the  machine,  which  increases  rapidly  with 
the  decrease  in  the  per  cent,  regulation  required.  If  worse 
regulation  is  permissible,  as  in  the  case  where  a  regulator  or  a 
suitable  compounding  device  is  used,  then  a  given  machine  can 
have  the  current  rating  considerably  increased,  but  in  order  to 
carry  this  current  deeper  slots  must  be  used  and  the  reactance 
thereby  increased. 

SINGLE  PHASE  MACHINES 

177.  Armature  Reaction  in  Single-phase  Machines.  —  Consider 
the  conditions  at  zero  power  factor;  the  current  lags  the  e.m.f. 
by  90  degrees  and  so  reaches  a  maximum  in  the  conductors  when 
these  conductors  lie  between  the  poles. 


i    h  i    t 


® 


3 

AT       '     |     '        S        ' 

A 

\ 
\ 
o                        c 

•) 

\T~ 

A         r        N        '          '       I 
B 

r 

* 


_SL 


J2L 


S        '    c  N  E 

FIG.  172. — Pulsation  of  the  armature  field  in  a  single-phase  alternator. 

A,  B  and  C,  Fig.  172,  show  the  position  of  the  poles  relative 
to  the  armature  when  the  current  has  the  values  given  at  instants 
1,  2  and  3  diagram  D.  It  may  be  seen  that  while  the  current 
passes  through  half  a  cycle  and  the  poles  move  through  one  pole 
pitch  the  flux  </>r,  due  to  the  armature  m.m.f.,  goes  through  half  a 
cycle  relative  to  the  armature  coils,  while  relative  to  the  poles  it 
changes  from  a  maximum  in  diagram  A  to  zero  in  diagram  B 
and  back  to  a  maximum  in  diagram  C,  and  so,  as  shown  in  curve 
a,  diagram  E,  is  pulsating  relative  to  the  poles  with  double  normal 
frequency. 

The  poles  are  surrounded  by  the  field  coils,  which  are  short- 
circuited  through  the  exciter,  and  any  pulsating  flux  in  the 
poles  induces  a  current  in  these  coils  which,  according  to  Lenz's 
law,  tends  to  wipe  out  the  flux;  thus  the  pulsation  becomes 


232  ELECTRICAL  MACHINE  DESIGN 

dampened  out,  as  shown  in  curve  6,  diagram  E.  The  armature 
field  is  therefore  equivalent  in  effect  to  a  constant  field,  which  is 
fixed  relative  to  the  poles  and  has  a  value  of  half  the  max  mum 
value  which  it  would  have  if  the  pulsation  were  not  dampened 
out. 

Another  way  to  look  at  the  above  subject  is  as  follows:  The 
armature  field  is  stationary  in  space  and  is  alternating.  Such  a 
field,  as  pointed  out  in  Art.  144,  page  184,  can  be  exactly  rep- 
resented by  two  progressive  fields  of  constant  value  which  move 
in  opposite  directions  through  the  distance  of  two  pole-pitches 
while  the  alternating  field  goes  through  one  cycle.  Consider 
these  two  fields  to  exist  separately,  then  one  moves  in  the  same 
direction  and  at  the  same  speed  as  the  poles  while  the  other 
moves  at  the  same  speed  but  in  the  opposite  direction  to  the  poles. 
The  former  is  therefore  stationary  with  regard  to  the  poles  and  may 
be  treated  in  exactly  the  same  way  as  the  armature  field  in  a 
polyphase  machine;  the  latter  field  revolves  at  the  same  speed 
as  the  main  poles  but  in  the  opposite  direction  and  so  causes  a 
double  frequency  pulsation  of  flux  in  these  poles  which  pulsa- 
tion induces  currents  in  the  field  windings  that  tend  to  wipe  out 
the  flux,  so  that  the  effect  of  this  latter  field  can  be  neglected 
in  a  discussion  of  armature  reaction. 

A  flux  of  double  frequency  in  the  poles  will  produce  a  third 
harmonic  of  e.m.f.  in  the  armature,  as  shown  in  Art.  144,  page 
184;  a  third  harmonic  of  current  in  the  armature  will  produce  a 
fourth  harmonic  oi  flux  in  the  poles  and  so  on;  however,  high 
frequency  harmonics  in  the  poles  are  so  well  dampened  out 
that  those  higher  than  the  third  can  be  neglected. 

The  demagnetizing  ampere-turns  per  pole  and  the  leakage 
reactance  are  worked  out  below  for  a  particular  case;  the  method 
is  quite  general,  but  since  the  result  depends  on  the  per  cent,  of 
the  pole-pitch  that  is  covered  by  the  winding,  no  general  formula 
is  deduced. 

178.  The  Demagnetizing  Ampere-turns  per  Pole  at  Zero  Power 
Factor. — Fig.  173  shows  the  distribution  of  the  m.m.f.  of  arma- 
ture reaction  for  a  machine  with  b  conductors  per  slot,  and  six 
slots  per  pole,  of  which  four  are  used,  at  the  instant  when  the 
current  has  its  maximum  value. 

If  the  pole  arc  =0.6  times  the  pole-pitch  then 
the   average  value  of  that  part  of  the  maximum  m.m.f.  which 
is  effective  X3.6^ 


ARMATURE  REACTIONS  IN  ALTERNATORS    233 
=  area  of  cross-hatched  curve  in  Fig.  173 


The  constant  field  which  is  fixed  relative  to  the  poles,  and  which 
is  the  only  one  that  need  be  considered  in  calculations,  has  a  value 
of  half  the  above  maximum  value,  therefore,  the  average  value 
of  the  part  of  this  constant  field  which  is  effective  =ATav  is 

such  that 


FIG.  173. — The  maximum  m.m.f.  of  a  single-phase  alternator  on  zero  power 

factor. 

and  AT av  =0.92  blm 

=  1.3  blc  where  Ic  is  the  effective  current 

0  effective  slots  per  pole 


=  0.32Xcond.  per  poleX/c. 


(30) 


179.  The  Leakage  Reactance. — As  in  the  case  of  the  polyphase 
machine  this  consists  of  end  connection,  slot  and  tooth-tip 
reactance. 

The  end-connection  reactance  =2xfpb2c2  ((f>eLe)  10~8  for  a 
machine  with  a  chain  winding,  and  half  of  this  value  for  a  ma- 
chine with  a  double-layer  winding;  where  c  is  the  effective  number 
of  slots  per  pole  or  the  number  which  carry  conductors. 

(j)eLe  is  found  from  Fig.  163,  but  it  must  be  noted  that  for  the 
type  of  winding  shown  in  Fig.  174,  (f>e  links  the  coils  of  four  slots 
and  the  length  of  the  end-connection  leakage  patl}  is  two-thirds 
of  the  value  which  it  would  have  if  all  the  slots  were  used;  the 
value  of  (f>eLe  is  therefore  3/2  times  that  found  from  Fig.  163. 

The  slot  reactance  = 


234 


ELECTRICAL  MACHINE  DESIGN 


,       3.2 /^     d2      2d3      d\  ,. 

where  $s  =  — (~-\ — -+—    -  +  —    :    the    slot    dimensions    are 
c    \3s      s      s  +  w     w/' 

given  in  Fig.  164,  page  218,  and  c  is  the  effective  number  of  slots 
per  pole. 


I    I 
I    I 


FIG.  174. — The  end  connection  leakage  path  in  single-phase  alternators. 


im 


FIG.  175. — The  positions  of  maximum  and  minimum  tooth  tip  leakage. 

The  tooth-tip  reactance  varies  from  a  maximum,  when  the 
conductors  are  in  position  A,  Fig.  175,  to  a  minimum,  when 
they  are  in  position  B.  In  the  former  position  it  may  be  seen 


ARMATURE  REACTIONS  IN  ALTERNATORS    235 

that  three  only  of  the  slots  lie  under  the  pole  at  any  time,  while 
in  the  latter  position  it  may  be  assumed  that  three  only  of  the 
slots  are  effective  since  the  leakage  lines  <j>0  which  link  all  the 
slots  have  to  pass  through  the  field  windings  and  are  therefore 
dampened  out. 

An  approximate  solution  for  the  case  of  a  machine  with  six 
slots  per  pole  of  which  four  are  used,  and  which  has  a  pole  arc  = 
0.6  times  the  pole-pitch,  is 
tooth-tip  reactance  =  2nfb2c2pLc  X (f>t  X  10~8 
where  <f)t  has  the  value  given  in  Art.  176,  page  223,  for  3  slots  per 
phase  per  pole  and  c  for  the  assumed  conditions  =  3. 

Example  of  Calculation. — Fig.  167  shows  the  actual  test  curves 
on  a  small  alternator  which  has  six  slots  per  pole  of  which  four 
are  used;  the  single-phase  short-circuit  curve  is  shown  dotted. 

The  demagnetizing  ampere-turns  per  pole 

=  0.32X12X4X62.5 

=  960  ampere-turns  per  pole 

the  corresponding  field  current 

_  demagnetizing  ampere-turns  per  pole 

field-turns  per  pole 
=  980 
420 
=  2.3  amperes 

The  reactance  per  phase 

££  +  te.  +  ^«)IrJ  10~8  ohms 


where  these  symbols  have  to  be  interpreted  in  the  light  of  the 
last  article 

J        T  O 

2^_-?=:(5Xl   from  Fig.  163)X~  since,  as   pointed    out   in  the 

2i  2i 

last  Art.  the  value  found  from  Fig.  163  has  to  be  increased 
50  per  cent,  because  four  only  of  the  six  slots  per  pole 
are  used 

3.2  /     1.5         0.25\ 
**   '-  ^  (3X075  +075r 


=2'3510^( 


1+ 


X 


(3X0.75)+(2X1) 
=  0.75 


236  ELECTRICAL  MACHINE  DESIGN 


c/>t   =0.52X0.75+0.42x10.7-4.9 
reactance  per  phase 

=  {2X7rX60Xl22X42X6  (7.5+0.8x6.5)  10~8} 
+  {2X7rX60Xl22x32X6  (4.9X6.5)  lO"8} 
=  1.6  ohms 

the  voltage  drop  per  phase  =  1.6X62.  5 

=  100  volts. 

with  this  value  and  with  the  demagnetizing  effect  =  2.  3  amp. 
the  triangle  abn,  shown  dotted  in  Fig.  167,  is  drawn  in  and  it 
may  be  seen  that  the  calculated  results  check  the  test  results 
very  closely. 

180.  Regulation  of  Single  -Phase  and  Three  -Phase  Alternators.— 
In  the  machine  whose  test  results  are  shown  in  Fig.  167  the  out- 
put at  full-load 

=  1.73X600X62.5  =  65  k.v.a.  for  the  three-phase  rating 
=  600  X62.5  =37.5  k.v.a.  for  the  single-phase  rating 

or  the  single-phase  output  is  about  60  per  cent,  of  the  three- 
phase  output.  For  this  ratio,  n  is  a  point  on  the  full-load 
saturation  curve  of  the  single-phase  machine  and  m  a  point 
on  that  of  the  three-phase  machine,  and,  as  may  be  seen,  the 
former  machine  has  the  better  regulation.  For  the  same  regu- 
lation in  each  case  the  single  phase  machine  may  be  given  65 
per  cent,  of  the  three-phase  rating. 


CHAPTER  XXII 
DESIGN  OF  A  REVOLVING  FIELD  SYSTEM 

The  problem  to  be  solved  in  this  chapter  is,  given  the  arma- 
ture of  an  alternator  and  also  its  rating  to  design  the  whole 
revolving  field  system. 


2         3        4.         5^  w  6     e  7         8   9    Q        10  Z  11  w  12  x  103 
Ampere  Turns  per  Pole 

FIG.  176. — Saturation  curves  for  a  400  k.v.a.  2400- volt,  3-phase,  60-cycle, 

600  r.p.m.  alternator. 

181.  Field  Excitation. — Fig.  176  shows  several  of  the  satura- 
tion curves  of  an  alternator: 
the  excitation  required  for  normal  voltage 

=  on  at  no-load 

=  oe   at  full-load  and  unity  power  factor 
=  og  at  full-load  and  85  per  cent,  power  factor 
=  ol    at  full-load  and  zero  power  factor 

237 


238  ELECTRICAL  MACHINE  DESIGN 

...  exciter  voltage 

the  maximum  exciting  current  =  t—     —  r-r  ..„,.,  —  TT-  and 

not  resistance  ot  field  coils 

the  maximum  excitation  =  max.    exciting    current  X  field- 

turns  per  pole 


The  radiating  surface  of  the  field  coils  should  be  large  enough 
to  keep  the  temperature  rise  with  the  excitation  og  below  that 
guaranteed,  which  is  generally  40°  C. 

The  maximum  excitation  om  should  be  large  enough  to  enable 
the  alternator  to  give  normal  voltage  on  all  loads  and  power 
factors  to  be  met  in  practice.  If  the  maximum  excitation  is 
equal  to  ol,  and,  therefore,  large  enough  to  maintain  normal 
voltage  at  full-load  and  zero  power  factor,  it  will  generally  be 
found  ample  for  all  ordinary  overloads  and  power  factors. 

The  field  resistance  should  have  such  a  value  that  the  max- 
imum excitation  om  may  be  obtained  with  the  normal  exciter 
voltage. 

The  ratio  —  -  is  about  1.25  for  normal  machines,  so  that  if 

og 

the  temperature  rise  with  excitation  og  is  40°  C.  that  with  exci- 
tation om  will  be  40X1.252  or  62°  C.     It  is  therefore  usual  to 
design  the  field  coils  for  an  excitation  om  and  for  a  temperature 
rise  of  65°  C. 
182.  Procedure  in  the  Design  of  a  Revolving  Field  System.— 

(a.)  Find  ATmax,  the  maximum  excitation  =  3  (armature  AT. 
per  pole)  for  a  first  approximation,  see  Art.  176,  page  230. 

(6.)  Find  M,  the  section  of  the  field  coil  wire  from  the  formula 

T...     A  Tmax  X  mean  turn 

M  =  —  -^j—       Formula  7,  page  65. 

volts  per  coil 

,,  .,     exciter  voltage 

where  the  volts  per  coil=—       —  ,  —        -  and  the  mean  turn  is 

poles 

found  as  follows: 

(f>a=ihe  flux  per  pole  crossing  the  gap=2  22kZf 

Formula  25,  page  190. 

If.j  the  leakage  factor,  is  assumed  to   be   1.2  for  a  first 
approximation. 

Pole  area  =  —  r-^i  —    .,     where  the  pole  density  at  normal 
pole  density 

voltage  and  frequency  and  at  no-load  is  taken  as  95,000  lines 
per  square  inch,  which  is  about  the  point  of  saturation.  The  pole 
area  also  =  0.95  XLPXWP. 


DESIGN  OF  A  REVOLVING  FIELD  SYSTEM      239 


Lp,  the  axial  length  of  the  pole,  is  made  0.5  in.  shorter 
than  the  frame  length  so  that  the  rotor  can  oscillate  f reejy.  The 
value  of  Wp,  the  pole  waist,  and  of  MT,  the  mean  turn  of  the 
coil,  can  then  be  found  approximately. 

(c)  Find  Lf,  the  radial  length  of  the  field  coil,  from  the  formula 
j   _  AT  max    r~  mean  turn 

1000   \ext.  periphery  X watts  per  sq.  in.  XdfXsf   XI. 27 
Formula  8,  page  66,  where: — 

external    periphery    is    found    approximately    from    the    pole 
dimensions; 


23456 
Peripheral  Velocity  of  Rotor  in  Ft.  per  Min. 


8xl03 


FIG.  177. — Heating  curves  for  the  field  coils  of  revolving  field  alternators. 

watts  per  square  inch  is  found  from  Fig.  177  which  gives  the 
results  of  tests  on  machines  similar  in  construction  to  that 
shown  in  Fig.  138,  and  with  the  type  of  field  coil  shown  in  Fig. 
140; 

df,  the  winding  depth,  is  chosen  so  as  to  give  the  most  econom- 
ical field  structure.  It  was  shown  in  Art.  56,  page  66,  that 
the  smaller  the  value  of  df  the  lower  the  cost  of  the  field  cop- 
per but  the  longer  and  more  expensive  the  poles.  The  most 


240 


ELECTRICAL  MACHINE  DESIGN 


economical  depth  can  be  found  by  trial  but  the  following  values 
may  be  used  as  a  first  approximation: 


Depth  of 

field  coil 

60-cycle 

25-cycle 

5  in 

0  6    in. 

10  in               

0.75  in. 

1.0    in. 

15  in 

1.0    in. 

1.25  in. 

20  in           

1.5    in. 

30  in                                        

2.0    in. 

40  in  

2.5    in. 

• 

For  a  given  pole-pitch  the  60-cycle  machine  runs  at  a  higher 
peripheral  velocity  than  the  25-cycle  machine,  it  therefore 
requires  less  radiating  surface  for  the  same  excitation  and  the 
poles  become  very  short  unless  the  value  of  df  is  decreased 
below  that  which  is  found  best  for  25-cycle  machines.  The 
above  figures  are  for  strip  copper  field  windings;  when  d.c.c. 
wire  is  used  the  above  depth  should  be  increased  about  20  per 
cent,  because  of  the  poorer  space  factor  of  this  type  of  winding, 
and  the  coils  should  be  tapered,  if  necessary,  as  shown  in  Fig.  140. 
(d)  Tf  is  the  number  of  field-turns  that  will  fill  up  the  space 
dfLf,  the  size  of  wire  being  fixed. 

183.  Calculation  of  the  Saturation  Curves. — It  is  necessary 
first  of  all  to  find  the  air  gap  clearance,  which  is  done  as  follows: 
The  approximate  number  of  ampere-turns  per  pole  required 
for  the  air  gap  at  no-load  and  normal  voltage,  namely  oq,  Fig. 
176  =  o?—  Iq  and  is  approximately 

=  A Tmax-l. 5 (armature  AT.  per  pole). 

Since  the  flux  per  pole  and  also  the  dimensions  of  the  machine 
are  given,  the  apparent  gap  density  and,  therefore,  the  air  gap 
clearance  required,  can  be  found  from  the  formulae 

flux  per  pole  crossing  the  gap 
Apparent  gap  density  = 


apparent  gap  density 
Air  gap  ampere-turns  =  ° 

Formula  3,  page  48. 


DESIGN  OF  A  REVOLVING  FIELD  SYSTEM      241 

The  magnetic  circuit  is  now  drawn  in  to  scale  and  the  leakage 
factor  and  the  no-load  saturation  curves  calculated  by  the 
method  explained  in  Arts.  46  and  47,  page  46. 

The  leakage  factor  at  full-load  and  zero  power  factor 

=  l  +  0m  /^g+<  + demagnetizing  AT.  per  po 

\  ATg  +  t 

212,  where  l.m  is  the  no-load  leakage  factor,  and 

the  demagnetizing    AT.  per  pole   =   0.35Xcond.  per  poleX/c. 

A  new  no-load  saturation  curve  is  calculated  using  the  above 
full-load  leakage  factor  and  plotted  as  shown  in  the  dotted  curve 
in  Fig.  176. 

The  reactance  per  phase  is  determined  from  the  formulae  on 
page  223  and  the  triangle  pqr  and  the  full-load  saturation  curve 
at  zero  power  factor  are  then  drawn  in. 

The  full-load  saturation  curves  at  other  power  factors  are 
calculated  by  the  use  of  the  diagram  shown  in  Fig.  169,  and  from 
these  curves  the  regulation  at  the  different  power  factors  is 
determined. 

If  the  regulation  found  from  the  curves  is  equal  to  or  slightly 
better  than  the  regulation  required,  then  the  field  design  is 
complete. 

If  the  regulation  found  is  considerably  better  than  that  re- 
quired, then  the  machine  is  unnecessarily  expensive  and  the 
following  changes  may  be  made: 

a.  The  air  gap  may  be  made  smaller  so  that  less  excitation  is 
required  and  the  cost  of  the  field  copper  is  reduced;  the  effect  of 
such  a  reduction  in  air  gap  is  explained  in  Art.  176,  page  229. 

b.  The  armature  can  be  redesigned  and  the  value  of  g,  the 
ampere  conductors  per  inch,  increased.     If  the  total  number  of 
conductors  is  increased,  the  flux  per  pole  is  decreased,  and  for 
the  same  tooth  density  and  a  reduced  value  of  flux  per  pole  the 
diameter  or  frame  length  or  both  must  be  reduced;  in  order  to 
carry  the  increased  number  of  ampere  conductors  on  each  inch  of 
the  periphery,  deeper  slots  must  be  supplied.     These  changes 
will   increase   both   the   armature   reaction   and   the   armature 
reactance  and  tend  to  make  the  regulation  worse,  but  will  make 
the  machine  cheaper. 

If  the  regulation  found  from  the  curves  is  worse  than  that 
required,  then  the  following  changes  may  be  made  on  the  machine 
to  improve  it: 

16 


242  ELECTRICAL  MACHINE  DESIGN 

c.  The  air  gap  may  be  increased  so  that  more  excitation  is  re- 
quired and  the  cost  of  the  field  copper  is  increased,  the  effect  of 
such  an  increase  in  air  gap  is  explained  in  Art.  176,  page  229. 

d.  The  air  gap  may  be  decreased  and  the  pole  section  reduced 
so  as  to  increase  the  pole  density  and  bend  over  the  saturation 
curve  as  shown  in  Fig.  170;  this,  however,  is  a  risky  expedient 
unless  all  the  material  that  goes  into  the  machine  is  carefully 
tested  for  permeability  and  rejected  if  not  up  to  standard.     If 
the  permeability  of  the  material  put  into  the  machine  is  lower 
than  was  expected  then  the  chances  are  that  the  machine  will 
not  be  able  to  give  its  voltage  on  low  power  factor  loads. 

e.  The  armature  can  be  redesigned  and  the  value  of  q,  the 
ampere  conductors  per  inch,  decreased,  this  will  have  an  effect 
opposite  to  that  discussed  in  section  b  and  will  require  a  more 
expensive  machine  but  will  give  better  regulation. 

Example. — The  armature  of  a  400-kv.a.,  2400-volt,  96-amp., 
3-phase,  60-cycle,  600-r.p.m.  revolving  field  alternator  is  built 
as  follows: 

Poles,  12 

Internal  diameter,  43  in. 

Frame  length,  12.25  in. 

Center  vent  ducts,  3  —  0.5  in. 
Slots  per  pole,  number,        6  open  type 

Slots  per  pole,  size,  0 . 75  X  2 . 0  in. 

Conductors  per  slot,  12 

Connection,  Y 

Exciter  voltage,  120 

It  is  required  to  design  the  revolving  field  system: 
The  armature  ampere-turns  per  pole 

cond.  per  slot      . 
=  slots  per  pole  X  —    — ~ —        X  /c 

=  6X6X96 
=  3450  ampere-turns. 
A  Tmax  =  the  maximum  excitation    =  3  X  3450 

=  10,400  ampere-turns,  approxi- 
mately. 

2400 
E  =  the  voltage  per  phase  ==^r~^  since  the  connection  is  Y 

1  .  10 

=  1380 

1380X108 
<f>a  =  the  flux  per  pole  =2.22 X  0.96 X  72  X  12X60 

3 

=  3.8X106 
If  =  the  leakage  factor,  is  assumed  to  be  =1.2. 


DESIGN  OF  A  REVOLVING  FIELD  SYSTEM      243 


=  48  sq.  in. 

Lp  =  the  axial  length  of  the  pole,  is  made  0  .  5  in.  shorter  than  the  frame 
length  and  =11.75  in. 

m  48  sq.  in. 

Wp=  the  pole  waist    -—L.- 


=  4.25  in. 

df,  the  depth  of  the  field  coil  =0.75  in.  from  the  table  on  page  240. 
MT  =  the  mean  turn  =  2(11.75  +  4.  25)  +  ?rX  1.25 

=  36  in. 
External  periphery  of  field  coil  =38  in. 

,,    ,,  ,  c  ,  ,  10,400X36 

M,  the  section  of  field  wire   =  —  -  —  ^  — 

=  37,500  circular  mils 
=  0.03  sq.  in. 

=  0.04  X  0.75  (strip  copper  wound  on  edge) 
Watts  per  square  inch  for  65°  C.  rise  =6.3  from  Fig.  177,  page  239. 

0  04 
sf.  the  space  factor  =  77- 

0.04  +  thickness  of  insulation 

=  0.8  using  paper  which  is  0.01  in.  thick 


T    xi         j-  i  i       ^u    *  £  u      M        10,400    /  36 

L/>  the  radial  length  of  field  coil    =  -*j^fr 


38X6.3X0.75X0.8X1.27 
=  4.75  in. 

4  75 
T7/,  the  number  of  turns  per  pole  =  -  ' 


0.05 
=  95  turns. 


The  maximum  exciting  current    = 


A  T  max 

~w~ 

10,400 


95 

=  110  amperes 

Maximum  output  from  exciter     =120X110 

=  13  kw. 
=  3.25  per  cent,  of  the  volt  ampere 

rating. 

AT g,  the  gap  ampere-turns  per  pole  at  normal  voltage  and  no-load, 
=  AT  max  —  1.5X  armature  AT.  per  pole,  approximately 
=  10,400-1.5X3450 
=  5200  ampere-turns. 

^,  the  pole  enclosure,  is  taken  as  0.65  which  is  an  average  value;  if  the 
pole  arc  be  made  too  large,  the  pole  leakage  becomes  excessive 
and  the  leakage  factor  high. 

3.8X106 
Ba,  the  apparent  gap  density    °n.25xp.65X  12.25 

=  42,500  lines  per  square  inch. 
5200X3.2 


X  C    = 


42500 
0.39  in. 


244 


ELECTRICAL  MACHINE  DESIGN 


C  =  the  Carter  coefficient    =1.12  from  Fig.  40,  page  44 
d    =  the  air  gap  in  inches    =0.35 

Calculation  of  the  leakage  factor: 

In  Fig.  178  h8  =   1.  in. 

L8  =11.75  in. 
l^  =   3.8  in. 
W8  =   7.0  in. 
hp  =   5.25  in. 
Lp  =11.75  in. 

Z3  =   5.2  in. 
Wp  =  4.25  in. 


and 


FIG.  178. — The  pole  dimensions. 
1X11.75 


("  X  7  \ 
1+2JX3^/ 


5.25X11.75 


and  <j>e  =  the  total  leakage  flux  per  pole 


=   40 
=   11  ATg+t 
=  77  ATg+t 

-   18ATg+t 
=  146  ATg+t 


The  value  of  ATg+t  =5200  ampere-turns  approximately,  since  the  tooth 
densities  in  alternators  are  so  low  that  the  ampere-turns  for  the  teeth  can 
be  neglected  here, 
therefore  <j>e  =  146 X  5200  =  760,000 

3.8X106  +  760000 
and  the  no-load  leakage  factor   =       — g  8xlQg — 

=  1.20 

The  full-load  leakage  factor,  at  zero  power  factor, 
5200  +  0.35X6X12X96^ 


200 


=  1.3 


DESIGN  OF  A  REVOLVING  FIELD  SYSTEM      245 


The  magnetic  areas: 

r     =  the  pole -pitch 

(/>   =  the  per  cent,  enclosure 

Lg  =  the  gross  iron 

Ln  =  the  net  iron 

A  g  =  the  apparent  gap  area 

C     =  the  Carter  coefficient 

At  =  minimum  tooth  area  per  pole 


=  11. 25  in. 

=  0.65 

=  10.75  in. 

=  9.6  in. 

=  90  sq.  in. 

=  1.12,  already  found. 

=  6X0.65X1.13X9.6. 

=  42.3  sq.  in. 


No-load  voltage  
Flux  per  pole  
Leakage  factor  

2400 

3  .  8  X  106 
1.2 

2700 
4.28X106 
1.2 

3000 
4.75X106 
1.2 

Length 

Area 

Density 

AT. 

Density 

AT. 

Density 

AT. 

Air  gap  

0.35 

90 
1.12 

42,500 

5200 

5850 

6500 

Teeth  
Pole  

Total  amp.-turn 

2.0 
6.0 

s  per  pole 

42.3         90,000 
47  .  5     j    96,000 

50 
325 

101,000 
108,000 

100 
960 

112,000 
120,000 

220 
2280 

5575 

6910 

9000 

To  get  the  figures  for  the  no-load  saturation  curve  with  the 
full -load  leakage  factor  it  is  necessary  to  recalculate  the  excita- 
tion for  the  poles,  using  a  leakage  factor  of  1.3;  the  air  gap  and 
teeth  are  not  affected. 


Pole  

6.0 

47.5 

105,000 

770 

119,000 

2220 

132,000 

5200 

Total  amp.  -turns  per  pole 

6020 

8170 

11,920 

From  the  former  set  of  values  the  no-load  saturation  curve  in 
Fig.  176  is  plotted  and  from  the  latter  set  the  dotted  curve,  which 
is  the  no-load  saturation  curve  with  the  full-load  leakage  factor, 
is  plotted. 

In  the  above  calculation  the  core  and  revolving  field  ring  have 
been  neglected  since  the  flux  density  is  very  low  in  the  case 
of  the  core  to  keep  down  the  temperature  of  the  iron  and  in  the 
case  of  the  field  ring  to  give  the  necessary  mechanical  strength 
and  rigidity. 

The  reactance  per  phase  is  found  by  the  method  shown  on 
page  224,  as  follows: 


246  ELECTRICAL  MACHINE  DESIGN 

=  5.3X3  from  Fig.  163-16 
3.2/  1.75       0.25 


1.13X1.12 
-- 


<£,       -0.52X0.87+0.42X5.8-2.9 
Reactance  per  phase 

-2X  7iX60  X122X22X  12(16  +  (1.7  +2.9)  X  12.25)  10-8 

=  1.88  ohms 

The  voltage  drop  per  phase  =  1.  88  X  96 

-180  volts 
The  voltage  drop  at  the  terminals  -  1  .73  X  180 

—  310  volts  since  the  winding 

is   Y-connected 

—  12.9    per    cent,    of    normal 

voltage 

The    demagnetizing    ampere-turns  per    pole—  0.35X6X12x96 

-2420 

and  the  corresponding  field  current  —  ..  ,  ,  , 

field-turns  per  pole 

—  25.5  amperes. 

The  full-load  saturation  curve  at  zero  power  factor  and  lagging 
current  can  now  be  drawn  in  and  is  shown  in  Fig.  176. 

The  curves  at  unity  power  factor  and  at  85  per  cent,  power 
factor  are  also  drawn  in  and  the  regulation  as  determined  from 
these  curves  —  9  per  cent,  at  unity  power  factor 

=  21  per  cent,  at  85  per  cent,  power  factor 
=  26  per  cent,  at  zero  power  factor. 


CHAPTER  XXIII 
LOSSES,  EFFICIENCY  AND  HEATING 

Many   of  the  losses   in  an  alternator  are  similar  to  and  are 
figured  out  in  the  same  way  as  those  in  a  D.-C.  machine. 

/  y,  \  3 

184.  Bearing  Friction  Loss  =  Q.Sldl(~)]  2  watts 

where  d  =  the  bearing  diameter  in  inches, 

l=the  bearing  length  in  inches, 
F&=the  rubbing  velocity  of  the  bearing  in  feet  per  minute. 

185.  Brush  Friction.  —  This  loss  is  small  since  there  are  few 
brushes  and  the  rubbing  velocity  is  low; 

y 

the  loss  =  1.25  A  -      watts 


where  A  is  the  total  brush  rubbing  surface  in  square  inches, 
V  r  is  the  rubbing  velocity  in  feet  per  minute. 

186.  Windage  Loss.  —  This  loss  cannot  be  separated  out  from 
the  bearing  friction  loss  so  that  its  value  is  not  known  and,  except 
in  the  case  of  turbo  generators,  it  can  be  neglected  since  it  is 
comparatively  small. 

187.  Iron  or  Core  Losses.  —  As  in  the  case  of  the  D.-C.  machine 
these  include  the  hysteresis  and  eddy  current  losses;  additional 
core  loss  due  to  filing,  to  leakage  flux  in  the  yoke  and  end  heads, 
and  to  non-uniform  distribution  of   flux  in  the  core;  losses  in 
the  pole  face. 

The  total  core  loss  is  figured  out  by  the  use  of  the  curves  in 
Fig.  81,  page  102,  which  curves  are  found  to  apply  to  alternators 
as  well  as  to  D.-C.  machines. 

188.  Excitation  Loss.  —  The  field  excitation  and  therefore  the 
field    excitation  loss  vary  with  the  power  factor,  as  shown  in 
Fig.  176.     The  loss  =  amperes  in  the  field  X  voltage  at  the  field 
terminals;  for  separately  excited  machines  the  rheostat  is  not 
considered  as  part  of  the  machine. 

247 


248 


ELECTRICAL  MACHINE  DESIGN 


189.  Armature  Copper  Loss. — 


Lb 


The  resistance  of  one  conductor  =  ™  ohms 

M 

and  the  loss  in  one  conductor  =    \*   watts 

M 

where  L&  is  the  length  of  one  conductor  in  inches, 
7c»is  the  current  in  each  conductor, 
M  is  the  section  of  each  conductor  in  cir.  mils. 

The  total  armature  copper  loss  =  Z<? 


b  c 


watts 


(31) 


where  Zc  is  the  total  number  of  conductors. 

In  addition  to  the  above  copper  loss  there  are  eddy  current 
losses  in  the  conductors  which  losses  may  be  large  and  cause 
trouble  due  to  heating  unless  care  is  taken  to  properly  laminate 
the  conductors. 


B  A 

FIG.  179. — Flux  in  an  armature  slot. 

Figure  179  shows  the  flux  distribution  in  the  slots  and  air  gap 
of  an  alternator.  The  flux  entering  a  slot  changes  from  a 
maximum  in  position  A  to  zero  in  position  B,  and  this  change 
of  flux  causes  eddy  currents  to  flow  in  the  conductors  in  the 
direction  indicated  by  crosses  and  dots.  To  prevent  these  eddy 
currents  from  having  a  large  value  it  is  necessary  to  laminate 
the  conductors  both  vertically  and  horizontally.  This  flux 
seldom  gets  beyond  half  the  depth  of  the  slot,  so  that  it  is  not 
important  to  laminate  conductors  which  lie  in  the  bottom  of 
the  slot. 

The  loss  due  to  these  eddy  currents  is  a  constant  loss,  being 
present  at  no-load  as  well  as  at  full-load,  and  is  therefore  measured 
with  the  core  losses. 

Of  greater  importance  are  the  eddy  currents  produced  by  the 
armature  leakage  flux.  Fig.  180  shows  the  leakage  flux  crossing 
an  alternator  slot  due  to  the  current  in  the  conductors.  This 
flux  is  alternating  and  therefore  sets  up  eddy  currents,  the  direc- 


LOSSES,  EFFICIENCY  AND  HEATING  249 

tion  of  which  is  indicated  at  one  instant  by  crosses  and  dots. 
To  prevent  these  eddy  currents  from  having  a  large  value  it  is 
necessary  to  laminate  the  conductors  horizontally. 

The  m.m.f.  tending  to  send  this  leakage  flux  across  the  slot  at 
mn  is  due  to  the  current  in  the  conductors  which  lie  below  mn, 
therefore  the  leakage  flux  density  is  zero  at  the  bottom  of  the 
slot  and  a  maximum  at  the  top  of  the  slot;  it  is  therefore  more 
important  to  laminate  the  conductors  in  the  top  of  the  slot 
than  those  in  the  .bottom. 

The  loss  due  to  leakage  flux  is  a  load  loss  since  the  leakage 
flux  which  produces  it  is  proportional  to  the  current  in  the 
conductors.  The  following  example  will  show  how  large  it 
may  become. 

Consider  the  case  of  the  double  layer  winding  shown  in  Fig. 

180;  the  flux  d<p  =  3.2(blc  X^}  X^ 
\          a/         s 

and  0,  the  flux  crossing  the  upper  layer  of  conductors 


Cd 

I   yXdy 
I    dXs 

Jd/2 


'm  j 


=  I.2bIcLcd 

s 

the  maximum  flux  crossing  the  upper  layer  of  conductors 

=  !.2bImLcXd 

s 

=  l.7bIcLcXd 

s 

Consider  a  loop  kl  of  width  g  and  thickness  dx,  the  effective 
e.m.f.  in  this  loop  due  to  the  flux  which  crosses  the  conductors 

=  4.44  <t>mflQ-8  volts 

the  resistance  of  this  loop 

1X2LC 

— - — --„  ohms 


the  eddy  current  in  the  loop 

_  effective  e.m.f. 
resistance 


250  ELECTRICAL  MACHINE  DESIGN 

4.44  X    l.7  X6/<XCXX/X  10-8 


2L, 


=  4.8  X  10~2X  blcx    XfXgXdx  amperes 
s 

and  the  current  density  in  the  loop 
_  current 
"  gXdx 

=  4.8XlO~2X&/cX-X/amp.  per  square  inch 

o 

the  normal  current  density  in  one  of  the  top  conductors 

1x2 

=  c  ''     ,  amp.  per  square  inch  approximately 
gXd 

and  the  ratio 

current  density  at  the  edge  of  conductor  due  to  slot  leakage 
normal  current  density 


s 
To  take  a  particular  example 

f=QO  cycles 


and  the  above  ratio  =  8 

The  eddy  currents  however  tend  to  wipe  out  the  flux  which  pro- 
duces them  so  that  the  above  result  is  greatly  exaggerated.1 

For  60-cycle  machines  the  depth  of  conductor  should  not 
exceed  0.5  in.  and  for  25-cycle  machines  should  not  exceed  0.75 
in.,  otherwise  trouble  is  liable  to  develop  due  to  heating  caused 
by  the  eddy  current  loss  in  the  conductors.  These  figures  rep- 
resent standard  practice  for  machines  up  to  2400  volts;  for  higher 
voltages  the  insulation  is  thick  and  the  difference  in  temperature 
between  the  copper  and  the  iron  quite  large;  due  to  additional 
eddy  current  losses,  this  temperature  difference  may  become 
excessive  and  cause  local  deterioration  of  the  insulation,  unless 
the  lamination  of  the  conductors  is  carried  much  further  than  in 
machines  for  low  voltages. 

1  For  an  accurate  solution  of  this  problem  see  Field,  Proc.  Amer.  Inst.  Elec. 
Engrs.,  Vol.  24,  page  765. 


LOSSES,  EFFICIENCY  AND  HEATING 


251 


190.  The  Efficiency. — For  an  alternating  current  generator 

~  .  output  in  kw. 

the  efficiency  =  -        — : — ^—  —. — - — 

output  m  kw.+ losses  in  kw. 

where  the  losses  are : 

Windage,  bearing  and  brush  friction; 

Excitation  loss; 

Iron  losses; 

Armature  copper  loss  (neglecting  eddy  current  loss); 

Load  losses,  which  are  principally  the  eddy  current  losses  in  the 

conductors. 


FIG.  180. — Eddy  currents  due  to  armature  slot  leakage. 

These  load  losses  are  determined  in  the  following  way : 
The  alternator  is  run  at  normal  speed  with  the  armature  short- 
circuited    through    an  ammeter,   it    is    then  excited  with    suf- 
ficient field  to  circulate  full-load  current  through  the  armature 
and  under  these  conditions  the  input  into  the  driving  motor  is 
measured;  the  field  is  then  taken  oft7  the  machine,  the  armature 
open-circuited,  and  the  power  taken  by  the  driving  motor  again 
measured;   the   difference   between  the  two  readings  is  called 
the  short-circuit  core  loss  and  includes: 
The  armature  PR  loss; 

The  eddy  current  loss  in  the  armature  conductors  due  to  leakage 
flux; 
The  small  iron  loss  due  to  the  flux  in  the  core. 


252  ELECTRICAL  MACHINE  DESIGN 

It  is  recommended  in  the  standardization  rules  ot  the  American 
Institute  of  Electrical  Engineers  that  the  load  losses  be  taken 
as  1/3  (short-circuit  core  loss  — the  PR  loss)  in  the  absence  of 
accurate  data  on  the  subject. 

191.  Heating. — The  temperature  rise  of  the  stator  of  a  revolv- 
ing field  alternator  is  limited  in  the  same  way  as  that  of  the  arma- 
ture of  a  D.-C.  machine. 

For  stator  cores,  built  with  iron  of  the  same  grade  as  used  in 
D.-C.  machines  and  of  a  thickness  =  0.014  in.,  the  following  flux 
densities  may  be  used  for  a  machine  whose  temperature  rise 
at  normal  load  must  not  exceed  40°  C. 

Frequency                 Maximum  tooth  density  Maximum  core  density 

in  lines  per  sq.  in.  in  lines  per  sq.  in. 

60  "cycles                                  90,000  45,000 

25  cycles                                110,000  65,000 

The  above  represent  standard  practice  for  open  slot  machines. 
When  the  slots  are  partially  closed,  so  that  the  tufting  of  the 
flux  in  the  air  gap  is  eliminated,  the  pole  face  losses  and  also 
the  eddy  current  losses  in  the  conductors  at  no-load  are  negligible 
and  the  densities  may  safely  be  increased  15  per  cent. 

The  end  connection  heating  is  limited  by  keeping  the  value  of 

.    amp-,  cond.  per  in.  .         .     „.      101       , 

the  ratio  — ^ — ~-  -  below  that  given  in  Fig.  181;   the 

cir.  mils  per  amp. 

curve  applies  to  revolving  field  open  type  machines. 

The  same  curve  is  used  for  both  chain  and  double  layer  windings; 
the  chain  winding  has  a  slightly  smaller  radiating  surface  than 
the  double-layer  winding  but  it  is»more  open  and  therefore  allows 
freer  circulation  of  air  between  the  coils. 

The  stator  heating  is  affected  by  that  of  the  rotor  because  the 
air  which  cools  the  stator  passes  over  the  rotor  surface,  during 
which  time  it  is  heated;  the  hotter  the  rotor  the  hotter  the  air 
which  is  blown  on  to  the  stator  and  the  greater  the  temperature 
rise  of  the  stator  above  that  of  the  air  in  the  power-house. 

The  ventilation  of  the  power-house  has  a  good  deal  to  do 
with  the  temperature  rise  of  the  machines  operating  therein. 
In  the  case  of  belt  driven  units  the  belt  keeps  the  air  in  the 
power-house  circulating;  the  flywheel  of  a  direct  connected 
engine  type  of  machine  has  the  same  effect.  In  the  case  of 
water-wheel  units,  however,  the  circulation  of  the  air  in  the 
power-house  has  generally  to  be  brought  about  by  the  machines 
themselves  and,  unless  they  are  built  with  fans,  so  as  to  prevent 


LOSSES,  EFFICIENCY  AND  HEATING 


253 


the  air  which  has  passed  through  the  machines  and  has  thereby 
become  heated  from  being  sucked  in  again,  they  will  often  get 
hot  even  although  liberally  designed.  Such  machines  generally 
stand  over  a  pit  and  it  will  often  be  found  that,  if  this  pit  is  con- 
nected by  a  duct  to  the  external  air,  the  temperature  rise  of  the 
machine  above  that  of  the  air  in  the  power-house  will  be  reduced. 
192.  Internal  Temperature  in  High  Voltage  Machines. — It 
was  pointed  out  in  Art.  94,  page  109,  that  the  difference  in 


1.4 


1.2 


£1.0 


0.6 


0.4 


1234567  8xlQ3 

Peripheral  Velocity  of  the  Rotor  in  Fl.per  Min. 

FIG.    181. — Heating   curve  for  stator  end   connections   of  revolving  field 

alternators. 


temperature  between  the  copper  in  the  center  of  a  machine  and 
that  on  the  end  connections,  if  all  the  heat  in  the  copper  is 
conducted  axially  along  the  conductors 


5.7X10-X 


cent. 


(cir.  mils  per  amp.): 
while  if  all  the  heat  is  conducted  through  the  slot  insulation  the 
difference  in  temperature  between  the  copper  and  the  iron 
_amp.  cond.  per  slot,  .thickness  of  insulation  .  1 
cir.  mils  per  amp. 


X 


, 


2d  +  s  " 0.003 

That  the  results  of  these  formulae  require  careful  consideration 


254  ELECTRICAL  MACHINE  DESIGN 

in  the  case  of  high  voltage  machines,  is  shown  by  the  following 
example. 

In  Art.  202  is  given  the  preliminary  design  of  a  2750  k.v.a. 
revolving  field  generator  for  direct  connection  to  a  water  wheel 
which  must  run  safely  at  an  overspeed  of  75  per  cent.  This 
overspeed  requirement  limits  the  diameter  of  the  machine  so 
that  the  frame  has  to  be  long  in  order  to  give  the  output. 

The  frame  length  =28.5  in. 

Insulation  thickness  =0.25  in.  for  11,000  volts. 

Slot  pitch  =2.8  in. 

Slot  width  =1.0  in. 

Slot  depth  =3. 5  in. 

Ampere  conductors  per  inch  =  700  assumed 

Circular  mils  per  ampere  =700  assumed. 

The  difference  in  temperature  between  the  copper  in  the 
center  of  the  machine  and  that  on  the  end  connections  if  all  the 
heat  is  conducted  along  the  conductor 

^5.7X104X(14.25)2 
7002 

=  24°C. 

the  difference  in  temperature  between  the  copper  and  the  iron 
if  all  the  heat  is  conducted  through  the  slot  insulation 

700X2.8  V0.25V     1 

X     r>      X; 


700        '    8    "  0.003 
=  29°C. 

In  such  a  case  a  large  part  of  the  copper  loss  will  be  conducted  to 
and  dissipated  by  the  end  connections,  and  in  order  that  these  may 

..     amp.cond.per  inch 

remain  cool  the  value  of  the  ratio     .       ., —  must  be 

err. mils  per  amp. 

taken  lower  than  that  given  in  Fig.  181,  and  the  temperature 
rise  on  the  end  connections  must  be  limited  to  about  30°  C.  at 
normal  load  in  order  that  the  copper  in  the  center  of  the  machine 
may  not  get  too  hot  and  char  the  insulation. 


CHAPTER  XXIV 
PROCEDURE  IN  DESIGN 

193.  The  Output  Equation. 

E   =  2.22  kZ(j>af  X  10~8  formula  25,  page  190. 


and  q 


2.l2xZx(Bg(fn:XLe)X-    ^     "XlO"8  taking  k  =  0.96 
nZIc 


therefore  nEI  =  the  output  in  watts 


,2.12X7T2X10-8  v 

12Q         -  XBrfLc  r.p.m.  gZV 

and  ft'  r   _  volt  amperes     5.7  X108 
Hf^mT"        ^B,^T 

The  value  of  5^;  the  apparent  gap  density,  is  limited  by  the 
permissible  value  of  Bt,  the  maximum  stator  tooth  density 
which,  as  pointed  out  in  Art.  191,  page  252,  is  approximately 

90,000  lines  per  square  inch  at  60  cycles 
110,000  lines  per  square  inch  at  25.  cycles 
for  open  slot  machines. 

Now  (f)a  =  Bt 
and   is 


therefore  Bg  =  Bt  X-,  X^ 

A         L/C 

The  ratio  y^  is  approximately  equal  to  0.75  taking  the  vent 

J^c 

ducts  and  the  insulation  between  the  laminations  into  account. 
The  ratio  -  varies  with  the  slot  pitch.     Suppose,  for  example, 

6 

255 


256  ELECTRICAL  MACHINE  DESIGN 

that  in  a  given  alternator  the  number  of  slots  is  halved;  since 
the  same  total  number  of  conductors  is  required  in  each  case, 
the  total  space  required  for  copper  remains  constant,  but  the 
space  required  for  slot  insulation  is  approximately  proportional 
to  the  number  of  slots  since  its  thickness  is  unchanged,  so  that 
when  the  number  of  slots  is  halved  the  slot  may  be  less  than  twice 

the  width  of  the  original  one;  the  ratio  —    —  therefore  increases 


as  the  slot  pitch  increases. 

The  slot  pitch  is  seldom  made  greater  than  2.75  in.  because 
the  section  of  the  copper  in  a  coil  for  such  a  slot  is  large  compared 
with  the  radiating  surface  of  the  coil  and  it  becomes  difficult  to 
keep  the  windings  cool. 

Figure  182,  which  shows  the  relation  between  -  =—  —  and  slot 

pitch  found  in  practice  for  open  slot  machines,  may  be  used  in 
preliminary  design. 

Bg  is  found  from  the  formula  given  above  and  is  plotted  against 
pole-pitch  in  Fig.  183,  a  reasonable  value  for  the  slot  pitch  being 
assumed. 

The  value  of  Bg  for  alternators  is  considerably  less  than  that 
found  for  D.-C.  machines  because  of  the  lower  tooth  density  in 
the  former  type  of  machine  due  to  the  fact  that  its  armature  is 
stationary  while  that  of  the  D.-C.  machine  is  revolving.  For 
a  given  output  and  speed,  therefore,  the  value  of  D2aLc  is  greater 
for  alternators  than  for  D.-C.  machines. 

The  value  of  q  is  limited  partly  by  heating  but  principally  by 
the  regulation  expected.  Suppose  for  example  that  for  a  given 
rating  the  value  of  q  is  increased,  which  can  be  done  by  increasing 
the  number  of  conductors  in  the  machine  or  decreasing  the  diame- 
ter. In  the  former  case  the  armature  reaction  will  be  increased 
since  it  is  proportional  to  the  number  of  conductors  per  pole  and 
the  armature  reactance  will  be  increased  since  it  is  proportional 
to  the  square  of  the  number  of  conductors  per  slot.  In  the  latter 
case  the  frame  length  must  increase  as  the  diameter  is  decreased 
in  order  to  carry  the  flux  per  pole  and  the  slots  must  be  made 
deeper  in  order  to  carry  the  larger  number  of  ampere  conductors 
on  each  inch  of  the  periphery,  both  of  which  changes  increase  the 
armature  reactance;  the  armature  reaction,  since  it  depends  on 
the  conductors  per  pole,  being  equal  to  0.35  X  cond.  per  pole 
X  Ic,  is  unchanged. 


PROCEDURE  IN  DESIGN 


257 


The  value  of  q  given  in  Fig.  184  may  be  used  for  a  first 
approximation  in  preliminary  design  and  will  give  reasonably 
good  regulation  if  the  ratio  of  field  excitation  at  full-load  and  zero 
power  factor  to  armature  ampere-turns  per  pole  be  not  less  than 
three,  and  the  pole  density  at  no-load  and  normal  voltage  be  about 
95,000  lines  per  square  inch. 

•g  60x10-1 


50 


3  40 

Hi 

a 
5  30 


20 


10 


Slot 
Slot  Width  in  Inches 

p  r  r  .^ 

CT  0  01  c 

32 

X 

X* 

^ 

f.\°N 

V 

S 

^ 

X*1 

^ 

x" 

t\v. 

^—  • 

>=* 

-- 

*^*^ 

ft1 

ot 

*—  -  * 

^~ 

+  —  • 

,—- 

x*" 

^ 

800 


400 
200 


0.5   1.0   1.5   2.0   2.5  ff  3.0 
Slot  Pitch  in  Inches 

FIG.  182. 


1 

i  C 

•<.:h 

/ 

or 

yvh 

/ 

^^ 

— 

/ 

x* 

5         10    -    15         20        25        3( 
Pole  Pitch  in  Inches 

FIG.  183. 

2.0 


51.5 


1.0 


20    40    60   80  100  A 

200   400   600   800  1000  B 

2000  4000  6000  8000  10000  C 
K.V.  A.  Output 

FIG.  184. 


\ 

\ 

\ 

X 

*--» 

—  . 

~— 

~— 

4          8          12        16        20        24 
Poles 

FIG.  185. 


Curves  used  in  preliminary  design. 

194.  The  Relation  between  Da  and  Lc. — There  is  no  simple 
method  whereby  Da2Lc  can  be  separated  into  its  two  components 
so  as  to  give  the  best  machine.  In  the  case  of  the  D.-C.  machine 
the  ratio  between  the  magnetic  and  the  electric  loading  was  used 
in  order  to  determine  Da  and  Lc  and  then  the  number  of  poles  was 
chosen  so  as  to  give  an  economical  shape  of  coil. 

The  number  of  poles  in  an  alternator  is  fixed  by  the  speed  and 
the  frequency,  and  the  diameter  and  length  of  the  machine  has 
to  be  chosen  so  as  to  give  an  economical  shape  of  coil.  If  for 

17 


258 


ELECTRICAL  MACHINE  DESIGN 


example  the  number  of  poles  on  a  given  diameter  be  increased,  the 
pole-pitch  will  be  reduced,  the  field  coil  will  become  more  and 
more  flattened  out,  and  a  point  will  finally  be  reached  at 
which  it  would  be  more  economical  to  increase  the  diameter  and 
shorten  the  length  of  the  machine  than  to  keep  the  diameter 
constant. 

Pole -pitch 

195.  Effect  of  the  Number  of  Poles  on  the  Ratio  — -  — . 

Frame  length 

Figure  186  shows  part  of  two  machines  which  are  duplicates  of 
one  another  so  far  as  the  pole  unit  is  concerned;  that  is,  they  have 


B 

FIG.  186. — Effect  of  the  number  of  poles  on  the  length  of  field  coils. 

the  same  pole-pitch,  air  gap,  armature  ampere-turns  per  pole  and 
field  ampere-turns  per  pole;  but  the  total  number  of  poles  is 
small  in  machine  A  and  large  in  machine  B.  It  may  be  seen 
that  in  the  former  machine  there  is  not  room  for  the  field  coils 
because  of  the  large  angle  between  the  poles.  In  order  to  get  the 
field  coils  on  to  the  poles  it  is  necessary  to  increase  the  diameter 
of  the  machine  without  increasing  the  radial  length  of  the  field 
coil,  that  is  without  increasing  the  armature  ampere-turns  per 
pole,  on  which  this  length  principally  depends,  so  that  the  same 
number  of  armature  ampere-turns  per  pole  must  now  be  put  on  a 
larger  pole-pitch  and  the  value  of  q,  the  ampere  conductors 
per  inch,  thereby  reduced.  Although  the  diameter  of  the 
machine  is  increased,  the  flux  per  pole  must  be  kept  constant 
otherwise  the  pole  waist  will  increase;  the  pole  arc  will  generally 


PROCEDURE  IN  DESIGN  259 

be  unchanged  and  the  ratio  — p  ?f  °n  will  decrease  as  the  di- 
ameter is  increased,  and  in  four-  and  six-pole  machines  will 
have  a  value  of  about  0.6. 

The  above  difficulty,  due  to  a  small  number  of  poles,  is 
more  apparent  in  machines  of  low  than  in  those  of  high  fre- 
quency, because  in  the  former  the  output  per  pole  is  generally 
larger,  for  example 

a  400-k.v.a.,  514-r.p.m.,  60-cycle  machine  has  14  poles  and  an 
output  of  28.5  k.v.a.  per  pole; 

a  400-k.v.a.,  500-r.p.m.,  25-cycle  machine  has  6  poles  and  an 
output  of  67  k.v.a.  per  pole; 

a  6  pole,  60-cycle  alternator  with  an  output  of  67  k.v.a.  per 
pole  would  have  a  rating  of  400  k.v.a.  at  1200  r.p.m.,  which 
would  be  as  difficult  to  build  as  the  above  25-cycle  machine  but 
is  such  an  unusual  rating  that  the  difficulty  seldom  occurs. 

The  value  of  q  in  Fig.  184  applies  to  machines  which  have 
more  than  10  poles;  for  machines  with  four  poles  this  value 
should  be  reduced  30  per  cent,  for  a  first  approximation,  and  for  a 
machine  with  six  poles  should  be  reduced  about  20  per  cent. 

Figure  185  shows  the  value  of  the  ratio  ~~^  ~ -^    generally 

frame  length    ' 

found  in  revolving  field  machines  when  the  diameter  is  not 
limited  by  peripheral  velocity,  and  may  be  used  in  preliminary 
design;  the  reason  for  the  increase  in  the  ratio  as  the  number 
of  poles  decreases  has  been  pointed  out  above. 
196.  Procedure  in  Design. 

volt  amperes    5.7X108  , 
DaLc=    ~^mT"        -£^  formula  32,  page  255 

and  frame  length  =  a  constant>  found  from  Fig.  185,  page  257, 

,  pole-pitch 

therefore  Lc  =  — 

a  constant 


pXa  constant 
,  n  3  _volt  amperes     5.7  Xl08XpX a  constant 

~~r^m7~  *XBaXfXq 

from  which  Da  may  be  found  approximately  since 
Eg  can  be  found  approximately  from  Fig.  183, 
q  can  be  found  from  Fig.  184, 
<f>  is  assumed  to  be  =0.65  for  a  first  approximation, 


260  ELECTRICAL  MACHINE  DESIGN 

the  constant  =  the  ratio  J-  -  T-   —  rr  from  Fig.  185. 

frame  length 

Tabulate  three  preliminary  designs,  one  for  a  diameter  20  per 
cent,  larger  than  that  already  found  and  the  other  20  per  cent. 
smaller. 

Find  the   probable   total  number  of    conductors  —  -  —  =  —  -  and 

LC 

assume  that  the  winding  to  be  used  is  single  circuit,  and  Y 
connected  if  three-phase,  so  that  Ic  —  the  full-load  line  current. 
Find  the  number  of  slots;  there  should  be  at  least  two  slots  per 
pole,  if  possible,  in  order  to  get  the  advantages  of  the  distrib- 
uted winding,  see  Art.  141,  page  180,  but  the  slot  pitch 
should  not  exceed  2.75  in.;  Art.  193,  page  256. 

-,.,,,  T  ,   ,       probable  total  conductors 

Find  the  conductors  per  slot  =—  —  r  --  e   i   .         —  :   take 

number  of  slots 

the  nearest  number  that  will  give  a  suitable  winding. 
Find  the  corresponding  total  number  of  conductors. 
Find  (/)a  from  the  formula  E   =   2.22  kZ$a  f  10~8  formula  25, 

page  190. 
Find  the  actual  frame  length  as  follows:    . 


a 

slot  Pltch  =  total  slots5 
divide  this  into  s  +  t  by  the  use  of  Fig.  182,  page  257; 

the  minimum  tooth  area  required  =  -  "    ,  -  r— 

max.  tooth  density 

where  the  max.  tooth  density  =90,000  lines  per  square  inch 

for  60  cycles 

110,000  lines  per  square  inch 
for  25  cycles 

for  open  slot  machines,  and  is  15  per  cent,  larger  for  machines 

with  partially  closed  slots; 

the  tooth  area  per  pole  =  slots  per  pole    X<f>XtXLn,  from 

which  Ln  can  be  found 


Lc=Lg  +  (ihe  center  vent  ducts),  where  these  ducts  are  0.5  in. 

wide  and  are  spaced  3  in.  apart. 
Find  d,  the  air  gap  clearance,  as  follows: 


ATX3.2 


•"•  •*•   Q 


PROCEDURE  IN  DESIGN 


261 


where  ATg  is  taken  as  1.5  (armature  ampere-turns  per  pole) 
for  a  first  approximation. 

The  field  is  now  designed  roughly  as  explained  in  Art.  182, 
page  238,  and  the  machine  drawn  out  to  scale,  after  which  the 
saturation  curves  are  calculated,  drawn  in,  and  the  regulation 
determined. 

If  the  regulation  is  better  or  worse  than  that  desired  from  the 
machine  then  the  design  must  be  changed  as  explained  in  Art. 
183,  page  241. 

Example. — Determine  approximately  the  dimensions  of  an 
alternator  of  the  following  rating: 

400  k.v.a.,  2400  volts,  3-phase,  60  cycle,  96  amperes,  600  r.p.m. 
The  work  is  carried  out  in  tabular  form  as  follows: 


Apparent  gap  density, 
Amp.  cond.  per  inch, 
Per  cent,  enclosure, 
Pole  pitch 


Bg  =42,000,  from  Fig.  183. 
q  =614,  from  Fig.  184. 
(j>  =0.65  assumed. 

=  0.95,  from  Fig.  185. 


,-,  ,        ,,  —  a  constant 

-t  rame  length 

Poles,  p  =12  for  600  r.p.m.  at  60  cycles. 

Armature  diameter,  Da  =43  in.,  from  formula  33,  page  259. 

Take  a  larger  and  a  smaller  diameter  so  that 
Armature  diameter,  Da  =43  in. 

Total  conductors,  probable,   Zc  =865 


Pole-pitch,  t=11.3in. 

Slots  per  pole  =6 

Total  slots  =72 

Cond.  per  slot  =12 

Connection  =Y 

Total  conductors,  actual,  Zc  =864 

Flux  per  pole,  <j>a  =3.8  X 106 

Slot  pitch,  A  =1.88  in. 

Slot  width,  s  =0.75  in. 

Minimum  tooth  width,  t  =1.13  in. 
Tooth  area  per  pole  required       =42.3  sq.  in. 

Net  axial  length  of  iron,  Ln  =9.6  in. 

Gross  length,  Lg  =10.6  in. 

Center  vent  ducts  =3-05  in. 

Frame  length,  Lc  =12.10  in. 

Apparent  gap  density,  Bg  =42,800 

Armature  AT.  per  pole  =3450 

A  Tg  assumed  =5200 

8C  =0.39 

Field  system: 
Maximum  AT.  per  pole,  ATmax  =10,400 


Leakage  factor,  assumed 
Pole  area  required 
Axial  length  of  pole, 
Pole  waist, 
Depth  of  field  coil, 
Mean  turn, 
External  periphery 
Exciter  voltage 
Section  of  wire, 


=  1.2 

=48  sq.  in. 
Lp  =11.6  in. 
Wp  =4.25  in. 
df  =0.75  in. 
MT=37  in. 
=39  in. 
=  120 
M  =38,500 

-0.04X0.75  in. 


36  in. 
725 
9.4  in. 


72 
10 
Y 
720 

4.56  X106 

1.57  in. 
0.67  in. 
0.9  in. 
51  sq.  in. 

14.5  in. 
16.1  in. 
5-0.5  in. 

18.6  in. 
40,200 
2880 
4300 
0.34 

8,600 

1.2 

58  sq.  in. 

18  in. 

3.4  in. 

0.75  in. 

47  in. 

49  in. 

120 

40,500 

0.04X0.8  in. 


52  in. 

1050 

13.6  in. 

6 

72 

14 

Y 

1008 

3.25  X106 

2.27  in. 

0.85  in.,  Fig.  182 

1.42  in. 

36  sq.  in. 

6.5  in. 
7.2  in. 
2-0.5  in. 
8.2  in. 
44,800 
4050 
6100 
0.44 

12,200 

1.2 

41  sq.  in. 

7.7  in. 

5.6  in. 
0.85  in. 
32  in. 
34  in. 
120 
39,000 
0.04X0.8  in. 


262  ELECTRICAL  MACHINE  DESIGN 

Watts  per  square  inch  =6.0  5.5        ,  6.5  page  239 

Space  factor,  s/=0.8  0.8  0.8 

Radial  length  of  field  coil,      Lf  =4.7  in.  4.0  in.  '5.2  in. 

The  three  machines  are  now  drawn  in  to  scale  as  shown  in 
Fig.  187. 

The  36-in.  machine  is  expensive  in  core  assembly  while  the 
52-in.  machine  is  expensive  in  inactive  material,  such  as  the 
material  in  the  yoke. 

So  far  as  operation  is  concerned  there  is  little  to  choose  be- 
tween the  machines.  The  armature  ampere-turns  per  pole  is  the 
same  fraction  of  the  field  ampere-turns  per  pole  in  each  case,  the 
voltage  drop  due  to  armature  reactance  is  also  about  the  same 
for  each  design.  In  the  36-in.  machine  the  air  gap  is  small 
and  the  length  Lc  is  large  which  tend  to  make  the  reactance 
large,  but  there  are  only  10  conductors  per  slot,  whereas  in  the 
52-in.  machine,  while  the  air  gap  is  larger  and  the  frame  length 
shorter,  the  number  of  conductors  per  slot  is  14;  the  reactance  is 
proportional  to  the  square  of  the  number  of  conductors  per  slot. 

The  36-in.  machine  is  rather  long  for  the  diameter  and  would 
be  difficult  to  ventilate  properly,  in  fact  it  would  probably  re- 
quire fans. 

Assume  that,  after  careful  consideration  of  the  weights  of 
the  three  machines  and  of  the  probable  cost  of  the  labor, 
which  latter  quantity  varies  with  the  size  of  the  factory  and 
its  organization,  the  43-in.  machine  is  chosen  as  the  most 
satisfactory;  it  is  now  necessary  to  complete  the  design  of  this 
machine. 

Winding 

96x864 
Amp.  oo  nd.  per  men          =—       ^-  =  614 


Amp.  cond.  per  in. 

n.  F     .,  =1.05  from  Fig.  181 

Cir.  mils  per  amp. 

Cir.  mils  per  amp.  =600 

Amp.  per  cond.  at  full  load  =96  < 

Section  of  conductor  =58,000  cir.  mils 

=  0.046  sq.  in. 

0.75  slot  width 

0.132  width  of  slot  insulation,  see  page  205. 

0.04    clearance  between  coil  and  core 

0.578  availaible  width  for  copper  and  insulation  on  conductor. 

Use  strip  copper  0.07  in.  wide  and  arrange  the  conductors  six  wide  in 

the  slot,  each  conductor  to  be  taped  with  half-lapped  cotton  tape  0.006 

in.  thick. 


PROCEDURE  IN  DESIGN 


263 


36  in. 


FIG.    187. — Comparative   designs  for  a  400   k.v.a.,    60-cycle,    600  r.p.m. 

alternator. 


264  ELECTRICAL  MACHINE  DESIGN 

section  of  cond.     0.046 


Depth  of  conductor 


width  of  cond.      0.07 
=  0.65  in. 


In  order  that  there  may  be  no  trouble  due  to  eddy  current  loss  caused 

by  the  slot  leakage  flux,  the  conductor  is  divided  into  two  strips  each 

0.325  in.  deep. 
Slot  depth  is  found  as  follows: 

0.325  depth  of  each  conductor 

0.024  insulation  thickness  on  each  conductor 

0.70    depth  of  two  insulated  conductors 

0.162  depth  of  slot  insulation  on  each  coil 

0.862  depth  of  each  insulated  coil 

2  number  of  coils  in  depth  of  the  slot 

1.72    depth  of  coil  space 

0.20    thickness  of  stick  in  top  of  slot 

2.0      depth  of  slot. 

Flux  density  in  the  core  =45,000  assumed 

Core  area  =53<feoOO  =42sq.in. 

core  area 

Core  depth  ——. —  =4. 5  in. 

net  iron 

External  dia.  of  armature  =  56  in. 

The  above  data  should  now  be  filled  in  on  a  design  sheet 
similar  to  that  shown  on  page  125. 

197.  Field  Design. — This  is  carried  out  as  shown  on  pages  242 
to  246,  where  the  field   system  for  the  machine  in  question  is 
designed    completely,    the    saturation    curves    determined    and 
drawn  in  and  the  regulation  found. 

198.  Variation  of  the  Length  of  a  Machine  for  a  Given  Di- 
ameter.— When  a  machine  for  a  new  rating  is  being  designed  it  is 
often  possible  to  save   considerable  expense  by  using  the  same 
punchings  as  on  a  machine  which  has  already  been  built,  and  ad- 
justing the  length  of  the  machine  to  suit  the  output  and  the 
fixed  diameter. 

Suppose  that  the  400  k.v.a.  machine  which  is  designed  in 
Art.  196  be  shortened  or  lengthened  50  per  cent.,  it  is  required  to 
find  the  output  that  may  be  expected  and  also  the  probable 
characteristics  of  the  machine.  The  essential  parts  of  the  three 
designs  are  tabulated  below. 

Armature  diameter 43  in.  43  in.  43  in. 

Frame  length 12.25  in.  8  in.  18.5  in. 

End  ducts 2-0.75  in.  2-0.75  in.  2-0.75  in. 

Center  ducts 3-0.5  in.  .         2-0.5  in.  5-0.5  in. 

Gross  iron...  10.75  in.  7.0  in.  16  in. 


PROCEDURE  IN  DESIGN  265 


Net  iron                                   9  6  in 

6.3  in. 

14.4  in. 

Slots  72 

72 

72 

Cond.  per  slot  12 

18 

8 

Size  of  cond 

2  (0.70X0.325  in.) 

0.09X0.325  in. 

2  (0.11X0.3  in.) 

Connection  

Y 

Y 

Y 

Amp.  cond.  per  inch.  .  . 

614 

614 

614 

Cir.  mils  per  ampere.  .  . 

600 

580 

580 

Arm.  AT.  per  pole  

3450 

3450 

3450 

Amperes  per  cond  96 

64 

144 

Terminal  voltage  per  ph.     2400 

2400 

2400 

Output  in  k.v.a 400  267  600 

The  above  machines  are  discussed  under  the  following  heads: 

Conductors  per  Slot. — Since  the  intention  is  to  use  the  same 
armature  punching,  the  number  of  slots  is  fixed,  and  for  the 
same  flux  density  in  the  different  machines  the  flux  per  pole  must 
be  directly  proportional  to  the  net  iron.  Now  the  voltage  per 
conductor  is  proportional  to  the  flux  per  pole,  so  that,  for  the 
same  terminal  voltage,  the  number  of  conductors  in  series  per 
phase  must  be  inversely  as  the  flux  per  pole  and  therefore  in- 
versely as  the  net  iron  in  the  frame  length. 

Size  of  Conductor. — For  the  same  total  copper  section,  this 
is  inversely  proportional  to  the  number  of  conductors  per  slot 
and  therefore  directly  proportional  to  the  net  iron  in  the  frame 
length. 

Current  Rating. — For  the  same  current  density  in  the  con- 
ductors the  current  in  each  conductor  must  be  proportional  to 
the  conductor  section  and  therefore  to  the  net  iron  in  the  frame 
length. 

Output. — For  the  same  voltage  in  each  case  the  output  in 
k.v.a.  is  proportional  to  the  current  and  therefore  to  the  net 
iron  in  the  frame  length. 

Air  Gap  Clearance. — The  current  per  conductor  is  inversely 
as  the  number  of  conductors  per  slot,  so  that  the  ampere  con- 
ductors per  slot  is  the  same  in  each  case,  and  the  armature 

,  .  ,        amp.  cond.  per  slot 
ampere-turns  per  pole,  which  =  -  —  X  slots  per 

2i 

pole,  is  independent  of  the  frame  length;  the  maximum  excitation 
and  the  air  gap  clearance  are,  therefore,  also  independent  of  the 
length  of  the  frame. 

Regulation. — The  demagnetizing  ampere-turns  per  pole 

=  0.35  X  cond.  per  pole  X  Ic 

and  since  Ic  is  inversely  proportional  to  the  number  of  conductors 
per  slot  the  demagnetizing  ampere-turns  per  pole  is  independent 
of  the  frame  length. 


266  ELECTRICAL  MACHINE  DESIGN 

The  armature  reactance  drop 

10-8X/ 


,L& 
where     *      is  independent  of  frame  length  since  it  depends  on 

the  pole-pitch,  which  is  constant, 
(f>s    is   the   same    in   each    case    since   the    slots    are 

unchanged, 
(fit     is  the  same  in  each  case  since  the  teeth  and  air  gap 

are  unchanged. 
The    armature    reactance    drop    is    therefore    proportional    to 

(cond.  per  slot)  2  X  current  X   (A  +  BLC) 
or  to  (cond.  per  slot)  (A  +  BLC) 

or  to  -  j  —  -—  —i  where  A  and  B  are  constants, 
L>c 

so  that  the  longer  the  machine  the  lower  is  its  reactance  drop 
and  the  better  the  regulation,  other  things  being  unchanged. 

The  pole  leakage  flux  consists  of  flank  leakage  which  is  constant 
and  pole-face  leakage  which  is  proportional  to  the  frame  length; 
<$>a,  the  flux  per  pole,  is  directly  proportional  to  the  frame  length; 

the  leakage  factor  =^a    ^e  =  —      —  c  where  C,  D  and  F  are  con- 

9a  fJLtc 

stants  and  so  is  smallest  for  the  longest  machine  that  is  built 
on  a  given  diameter. 

A  machine  cannot  be  lengthened  indefinitely,  however,  because 
a  point  is  finally  reached  at  which  it  becomes  impossible  to  cool 
the  center  of  the  core  without  a  considerable  modification  in 
the  type  of  construction  and  the  addition  of  fans,  and  still 
further,  as  the  length  increases  the  pole  section  departs  more 
and  more  from  the  square  section. 

199.  Windings  for  Different  Voltages.  —  The  armature  of  a 
400-k.v.a.,  2400-volt,  96-ampere,  3-phase,  60-cycle,  600-r.p.m. 
alternator  is  built  as  follows: 

Internal  diameter,  43  in. 

Frame  length,  12.25  in. 

Slots,  number,  72 

Slots,  size,  0.75  in.  X  2.0  in. 

Conductors  per  slot,  number,     12 

Conductors  per  slot,  size,  2(0.07  in.  X  0.325  in.) 

Connection,  Y 

It  is  required  to  design  armature  windings  for  the  following 
voltages  : 


PROCEDURE  IN  DESIGN  267 


600  volts,  3-phase,  60  cycles, 
2400  volts,  2-phase,  60  cycles. 
To  find  the  Conductors  per  Slot. 
E   =  2.22kZ<f>aflO-* 

=  a  constant  X  &  X  cond.  per  slot  X 


phases 


cond.  per  slot  .          .        .. 

=  a  constant  X  k  X  -    —  r^         —  for  a  given  frame  and 

phases 

frequency. 

For  the  machine  in  question  k    =  0.966  for  a  3-phase  winding 

=  0.911  for  a  2-phase  winding 
volts  per  phase  X  phases 


and  the  constant  = 


A; X  cond.  per  slot 

2400  X  3 
1.73Xd 


0.966X12 
=  360 

For  the  600-volt,  3-phase  winding 

volts  per  phaseX  phases 
cond.  per  slot  =  —    — -f- — — 

A;  X  a  constant 

600X3 


0.966X360 
=  5.2,  or  say  5,  if  600  is  the  voltage  per  phase,  that 

is  if  the  winding  is  A  connected 
600 


1.73 

and 


X3 


0.966X360 
f*r\(\ 

=  3.0  if  Y^T^  is  the  voltage  per  phase,  that  is  if 
1.7o 

the  winding  is  Y  connected. 

The  Y  connected  winding  is  the  better  of  the  two  because  with 
such  a  connection  any  third  harmonic  in  the  e.m.f.  wave  is  elimi- 
nated, whereas  in  the  case  of  a  A  connected  winding  the  third 
harmonics  cause  a  circulating  current  to  flow  in  the  closed  circuit 
of  the  delta. 

Since  the  winding  is  double  layer,  the  number  of  conductors 
per  slot  must  be  a  multiple  of  two,  so  that  the  winding  actually 
used  will  have  six  conductors  per  slot  and  will  be  connected  two 
circuit. 

For  the  2400-volt,  2-phase  winding 


268 


ELECTRICAL  MACHINE  DESIGN 


volts  per  phaseX  phases 
cond.  per  slot=—    — -f- — — 

#Xa  constant 

2400X2 
0.911X360 

=  14.7 

In  order  to  use  15  conductors  per  slot  it  will  be  necessary,  if 
the  winding  is  double  layer,  to  use  30  conductors  per  slot  and 
connect  the  winding  two  circuit,  and  the  size  of  each  conductor 
will  be  small;  it  will  be  preferable  to  use  14  conductors  per  slot, 
for  which  number  the  flux  density  in  the  machine  is  5  per  cent, 
higher  than  for  the  original  2400-volt,  3-phase  winding. 

To  find  the  Size  of  Conductor.  In  order  that  the  stator  loss  and 
stator  heating  be  the  same  in  each  case  it  is  necessary  to  keep  the 

,.    amp.  cond.  per  inch  ,   . 

ratio — -. -, —  -  constant;  the  work   is  carried  out  in 

cir  mils  per  amp. 

tabular  form  as  follows: 


rt 

a 

g 

ft 

8 

1 

"d  & 

*   d 

"5 

if 

I 

<3  c 

8 

aS   d 

O 

O     C 

o    c 

1| 

•* 

£l 

Hi 

a 

N 

j-S 

O 

fl 

•Bl 

< 

0 

CO 

400 

2400 

3 

96 

Y 

96 

12 

2(0.07X0.325  in.) 

614 

600 

400 

600 

3 

384 

YY 

192 

6 

4(0.07X0.325  in.) 

614 

600 

400 

2400 

2 

83 

1  circuit 

83 

14 

2(0.055X0.325  in.) 

620 

550 

It  may  be  seen  from  the  value  of  circular  mils  per  ampere 
that  the  two-phase  machine  will  get  about  10  per  cent,  hotter  than 
the  three-phase  machines  because  it  is  not  possible  to  get  sufficient 
copper  into  the  slot  for  this  rating.  This  trouble  is  inherent  to 
the  two-phase  machine  because,  for  a  given  frame,  rating  and 
terminal  voltage 

cond.  per  slot— 2  phase _  Et  X  2  X  1 .73  X  0.966 
cond.  per  slot — 3  ph.  Y.~ 

1 


0.911X^X3 

current  per  cond. — 2  phase_k.w.     1. 
current  per  cond. — 3  ph.Y.      2Et       k.w. 


=  1.22 


1.16 


that  is  to  say,  the  number  of  conductors  per  slot  for  the  two-phase 
rating  is  22  per  cent,  greater  than  that  for  the  three-phase  rating, 
while  the  current  per  conductor  is  reduced  only  16  per  cent. 

200.  Example  of  a  Machine  with  Field  Coils  of  D.  C.  C.  Wire.— 
The  following  is  a  preliminary  design  for  a  75-k.v.a..  2400-volt, 
3-phase,  18-ampere,  60-cycle,  1200-r.p.m.  alternator. 


PROCEDURE  IN  DESIGN  269 

Apparent  gap  density,  Bg  =  42,000,  from  Fig.  183 

Amp.  cond.  per  inch,  <?  =  450;  20  per  cent,  lower  than  the  value 

from  Fig.  184;  see  Art.  195,  page  258. 
Per  cent,  enclosure,  ^  =  0.65,  assumed 

Pole  pitch 

^ —  — rr-  =  a  constant  =1.6,  from  Fig.  185 

Frame  length 

Poles,  p  =  6  for  1200  r.p.m.  at  60  cycles 

Armature  diameter,  Z)a=21in. 

Total  conductors,  probable,     Zc  =  1650 

Pole  pitch,  T  =  ll  in. 

Slots  per  pole  =6 

Total  slots  =36 

Cond.  per  slot  =46 

Connection  Y 

Total  conductors,  actual  =1656 

Flux  per  pole,  </>«  =  2.0X  106 

Slot  pitch,  ^  =  1.83 

Slot  width,  s  =  0.75,  from  Fig.  182 

Minimum  tooth  width,  /  =  1.08 

Tooth  area  per  pole  required      =22.2  sq.  in. 

Net  axial  length  of  iron,  Ln  =  5.3  in. 

Gross  length,  Z/g  =  5.9  in. 

Center  vent  ducts  =1-0. 5  in. 

Frame  length,  Lc  =  6.4in. 

Apparent  gap  density,  .60  =  43,600 

Armature  AT.  per  pole  =2480 

ATg  assumed  =3700 

dC  =0.27  in. 

• 

Field  system. 

Maximum  AT  per  pole,  ATmax  =  7500 

Leakage  factor  assumed  =1.2 

Pole  area  =25.5  sq.  in. 

Axial  length  of  pole,  Z/p=6.0in. 

Pole  waist,  TFP  =  4.5  in. 

Depth  of  field  coil,  d/  =  1.0  in.,  assumed 

Mean  turn  =25  in. 

External  periphery  =29  in. 

Exciter  voltage  =120 

Section  of  field  wire  =9500  cir.  mils.     Use  No.  11  square  B.  &  S. 

gauge  which  has  a  section  of   10,500 

cir.  mils. 

Watts  per  square  inch  =4.7,  page  239. 

Space  factor  =0.86 

Radial  length  of  field  coils,     L/  =  3.25  in. 

The  field  coil  as  designed  with  a  uniform  thickness  of  1  in. 
is  shown  dotted  in  Fig.  188,  the  actual  shape  of  coil  used  is  shown 
by  heavy  lines. 


270 


ELECTRICAL  MACHINE  DESIGN 


201.  Design  of  a  25 -cycle  Alternator. — Two  designs  are 
given  below  for  an  alternator  of  the  following  rating;  400  k.  v.  a.; 
2400  volts,  3  phase,  96  amperes,  25  cycle,  500  r.p.m. 

In  the  first  design  the  value  of  ampere  conductors  per  inch  is 
taken  from  Fig.  184,  in  the  second  design  a  value  20  per 'cent, 
lower  is  used  and  the  per  cent,  enclosure  is  also  reduced. 


FIG.  188. — Field  system  of  a  75  k.v.a.,  60-cycle,  1200  r.p.m.  alternator. 


Apparent  gap  density,  £y 

Amp.  cond.  per  inch,   *  g=614 

Per  cent,  enclosure,  ^  =  0.65 

Pole  pitch 

— TV  =  a  constant  =1.6 
Frame  length 

Poles,  p  =  6 

Armature  .diameter,  Da  =  41  in. 
Probable  total  conductors,  Zc  =  820 

Pole-pitch,  T  =  21.5in. 

Slots  per  pole  =9 

Total  slots  =54 

Cond.  per  slot  =15 

Connection                        •  =Y 

Total  conductors,  Zc  =  810 

Flux  per  pole,  <f>a  =  9.7 X  106 

Slot  pitch,  X  =  2.39  in. 

Slot  width,  s  =  0.9in. 

Minimum  tooth  width,  /  =  1.49  in. 
Tooth  area  required  per  pole  =  88  sq.  in. 

Net  axial  length  of  iron,  Ln  =  10  in. 

Gross  iron,  Lg  =  ll  in. 

Center  vent  ducts  =3-0.5  in. 

Frame  length,  Lc  =  12.5  in. 

Apparent  gap  density,  Bg  =  55, 000 

Armature  AT  per  pole  =6500 

A  Tg  assumed  =9750 

C  =0.57 


52,000 
510 
0.6 

1.6 


6 

44  in. 

730 

23  in. 

9 

54 

13 

Y 

702 

11.2X106 

2.56  in. 

0.9  in. 

1.66  in. 

102  sq.  in. 

11. 4  in. 

12.7  in. 

3-0.5  in. 

14.2  in. 

57,000 

5600 

8400 

0.47 


PROCEDURE  IN  DESIGN 


271 


Field  system. 

Maximum  AT.  per  pole 
Leakage  factor  assumed 
Pole  area 

Axial  length  of  pole, 
Pole  waist, 
Depth  of  field  coil, 
Mean  turn 
External  periphery 
Section  of  wire 


=  19,500 
=  1.2 

=  120  sq.  in. 
=  12in. 


=  50  in. 

=  55  in. 

=  49,000. 

=  0.026in.X  1.5  in. 


16,800 

1.2 

142  sq.  in. 

13.7  in. 

11  in. 

1.5  in. 

55  in. 

60  in. 

46,000. 

0.024  in.  X  1.5  in. 


This  wire  is  difficult  to  bend,  therefore  use  a  double  layer  winding  and 

conductors  of  section  0.052  in.  X  0.75  in.      0.048  in.  X  0.75  in. 

Watts  per  square  inch  =4.6.  4.2,  page  239 

Space  factor  =0.86.  0.86. 

Radial  depth  of  field  coil         =7.3  in.  6.1  in. 

Part  of  each  machine  is  drawn  to  scale  in  Fig.  189  and  it  may 
be  seen  that  the  first  design  is  an  impossible  one  unless  modified; 
the  field  coils  may  be  made  shorter  but  then  the  radiating 
surface  will  be  reduced  and  the  temperature  rise  of  the  field 
coils  be  too  great  or  they  may  be  made  of  d.c.c.  wire  and  tapered 
off  as  shown  in  Fig.  188. 


FIG.  189. — Field  system  of  a  400  k.v.a.,  25-cycle,  500  r.p.m.  alternator. 

It  must  not  be  imagined  that  the  designs  which  have  been 
worked  out  in  this  chapter  are  the  only  possible  ones  that 
might  have  been  used.  If  the  regulation  expected  from  the  ma- 
chine differs  from  that  obtained  from  the  particular  design  which 
has  been  worked  out  then  a  radical  change  in  that  design  will  be 
necessary,  but  when  one  design  has  been  worked  out  completely 
and  its  characteristics  determined  the  changes  necessary  to  meet 
certain  requirements  can  readily  be  determined. 


CHAPTER  XXV 
HIGH-SPEED  ALTERNATORS 

202.  Alternators  Built  for  an  Overspeed. — A  typical  example 
of  such  a  machine  is  an  alternator  which  is  direct  connected 
to  a  water-wheel. 

The  peripheral  velocity  of  a  water-wheel  is  less  than  the 
velocity  of  the  operating  water;  if  the  load  on  such  a  machine 
be  suddenly  removed,  and  the  governor  does  not  operate  rapidly 
enough,  then  the  machine  will  accelerate  until  it  runs  with  a 
peripheral  velocity  which  is  approximately  equal  to  the  velocity 
of  the  water  and  is  from  60  to  100  per  cent,  above  normal,  de- 
pending on  the  type  of  wheel  used. 

An  alternator  which  is  direct  connected  to  a  water-wheel  must 
have  a  diameter  small  enough  to  allow  the  machine  to  run  at  the 
above  overspeed  without  the  stresses  due  to  centrifugal  force 
becoming  dangerous.  When  this  diameter  has  been  reached, 
the  output  for  a  given  speed  can  be  increased  only  by  increasing 
the  length  of  the  machine,  and  after  a  certain  length  has  been 
reached  it  becomes  impossible  to  keep  the  center  of  the  machine 
cool  without  the  use  of  special  methods  of  ventilation. 

Example. — Determine  approximately  the  dimensions  of  an 
alternator  of  the  following  rating : 

2750  k.v.a.,  2400  volts,  three  phase,  660  amperes,  60  cycles, 
600  r.p.m.;  the  machine  has  to  run  at  an  overspeed  of  75  per 
cent. 

If  the  design  were  carried  out  in  the  usual  way  then  the 
following  would  be  the  result. 

Apparent  gap  density,          £0  =  43,000. 
Amp.  cond.  per  inch,  q  =  72Q. 

Per  cent,  enclosure,  ^=0.7. 

Pole-pitch 

— T-  =a  constant         =0.95. 
Frame  length 

Poles,  p  =  12. 

Armature  diameter,  Da  =  76  in. 

With  this  diameter  the  peripheral  velocity  at  600  r.p.m. 
would  be  12,000  ft.  per  minute  and  the  peripheral  velocity  at 

272 


HIGH  SPEED  ALTERNATORS  273 

the  overspeed  would  be  21,000  ft.  per  minute.  At  such  a  speed 
the  stresses  due  to  centrifugal  force  are  so  large  that  it  is  difficult 
to  build  a  safe  rotor. 

With  the  type  of  construction  shown  in  Fig.  190,  a  safe  and 
comparatively  cheap  machine  can  be  built  with  a  peripheral 
velocity  of  17,500  ft.  per  minute,  which  corresponds  to  a  pe- 
ripheral velocity  of  10,000  ft.  per  minute  under  normal  running 
conditions,  and  a  maximum  diameter  of  64  in.  for  the  machine 
in  question. 

The  design  can  now  be  continued  as  follows: 

Armature  diameter,  Da  =  64in. 

Total  conductors  (probable)  Zc  =  220. 

Pole-pitch,  T  =  16.8  in. 

Slots  per  pole  =  6. 

Total  slots  =  72. 

Conductors  per  slot  =3.0;  use  6  cond.  per  slot  and  connect  the 

winding  two  circuit  Y. 
Total  conductors  (actual),     Zc  =  216. 
Flux  per  pole,  <£a  =  15.2  X  106. 

Slot  pitch,  A  =  2.8  in. 

Slot  width,  s  =  0.95  in. 

Tooth  width,  /  =  1.85  in. 

Tooth  area  required  per  pole      =169  sq.  in. 
Net  axial  length  of  iron,       Z/n  =  21.7in. 
Gross  length  of  iron,  Lg  =  24.25  in. 

Center  vent  ducts  =9-0.5  in. 

Frame  length,  Lc  =  28,75  in. 

The  remainder  of  the  design  is  carried  out  in  the  usual  way 
and  the  machine  is  then  drawn  to  scale  as  shown  in  Fig.  190, 
which  shows  the  kind  of  ventilation  required  to  keep  the  center 
of  the  machine  cool.  Fans  are  placed  at  the  ends  of  the  rotor 
to  create  an  air  pressure  and  so  force  air  out  across  the  back  of 
the  punchings  and  also  through  the  vent  ducts.  Coil  retainers 
are  put  at  A  to  prevent  the  rotor  coils  from  bulging  out  due  to 
centrifugal  force. 

203.  Turbo  Alternators. — Alternators  which  are  direct  con- 
nected to  steam  tubines  run  at  a  high  speed  and  have  therefore 
few  poles,  even  for  large  ratings.  It  was  pointed  out  in  Art. 
195,  page  258,  that  when  the  number  of  poles  is  small  it  becomes 
difficult  to  find  space  for  the  necessary  field  copper,  but  that  this 
difficulty  could  be  overcome  by  increasing  the  diameter  of  the 
machine  and  lowering  the  value  of  q,  the  ampere  conductors 
per  inch. 

18 


274 


ELECTRICAL  MACHINE  DESIGN 


In  the  case  of  the  turbo  alternator  the  diameter  cannot  be 
increased  beyond  the  value  at  which  the  stresses  in  the  machine 
due  to  centrifiugal  force  reach  their  safe  limit,  and  some  other 
method  of  solving  the  difficulty  must  be  found. 

The  number  of  ampere-turns  per  pole  on  the  field  may  be 
reduced  below  that  desired,  without  changing  the  armature 
design,  but  this,  as  pointed  out  in  Art.  176,  page  229,  will  cause 
the  regulation  of  the  machine  to  be  poor. 


FIG.   190.— Outline  of    a  2750    k.v.a.,  600    r.p.m.,  60-cycle,  water  wheel 
driven  alternator,  to  run  at  75  per  cent,  overspeed. 

The  number  of  ampere-turns  per  pole  may  be  reduced  below 
the  value  desired,  on  both  field  and  armature;  then  the  regulation 
may  be  good,  but,  since  the  number  of  conductors  is  reduced, 
the  flux  per  pole  will  be  increased  for  the  same  rating,  the 
machine  must  therefore  be  lengthened  to  keep  down  the  flux 
density  and  so  will  be  expensive. 

The  number  of  ampere-turns  per  pole  on  both  armature  and 
field  may  be  left  as  desired  and  the  field  coils,  allowed  to  run  hot; 
then  the  regulation  may  be  good  and  the  machine  not  too 
expensive,  but  it  will  be  necessary  to  use  materials  such  as  mica 
and  asbestos  for  the  field  insulation  so  that  it  will  not  deteriorate 
due  to  the  high  temperature.  With  such  insulation  it  is  usual 
to  design  the  field  coils  for  a  temperature  rise  by  resistance  of 
100°  C.  at  the  maximum  field  excitation;  this  corresponds  to  an 
increase  in  resistance  of  about  40  per  cent. 


HIGH  SPEED  ALTERNATORS  275 

204.  Rotor    Construction  for  Turbo  Alternators.  —  Due  to  the 

high  peripheral  velocities  required  for  turbo  alternators  the 
centrifugal  force  acting  on  a  body  at  the  rotor  surface  of  such  a 
machine  is  very  large,  for  example,  a  weight  of  1  Ib.  revolving  at 
1800  r.p.m.  with  a  peripheral  velocity  of  20,000  ft.  per  minute 
is  acted  on  by  a  centrifugal  force  of  2000  Ib.  It  is,  therefore, 
necessary  to  adopt  a  strong  type  of  construction;  one  which 
can  be  well  balanced  and  which  will  stay  in  good  balance  indefi- 
nitely; that  is,  the  rotor  windings  must  be  rigidly  held  so  that 
they  cannot  move.  The  type  of  construction  shown  in  Fig.  191 
fulfills  the  above  conditions  and  has  also  the  additional  advan- 
tage that  since  there  are  no  projections  on  the  rotor  surface  the 
windage  loss  and  the  noise  due  to  stirring  up  of  the  air  are  a 
minimum. 

205.  Stresses  in  Turbo  Rotors.  —  The  electrical  and  mechanical 
design  of  a  turbo  rotor  must  be  carried  out  together,  because 
the  space  available  for  field  copper  cannot  be  determined  until 
the  section  of  steel  below  the  rotor  coils,  required  for  mechanical 
strength,  has  been  fixed.     The  most  important  of  the  stresses  in 
the  type  of  rotor  shown  in  Fig.  191  are  determined  approximately 
as  follows: 

Stress  at  the  Bottom  of  a  Rotor  Tooth. 

Assume  that  one  tooth  carries  the  centrifugal  force  due  to  its 
own  weight  and  to  that  of  the  contents  of  one  slot,  and  also  that 
the  total  weight  of  copper,  insulation  and  wedge  in  a  slot  is  the 
same  as  that  of  an  equal  volume  of  steel. 

Consider  one  inch  in  axial  length  of  the  rotor,  then  in  Fig.  192, 
where  all  the  dimensions  are  in  inches, 

dw  =  2xr  ^^.XdrXQ.28  Ib.  =  weight  of  the  cross-hatched  piece 

oDU 

v  =   12  x     60~  =tne  PeriPneral  velocity  of  this  piece; 

,   .,  dwXv2Xl2 

the  centrifugal  force  due  to  dw=-~ 

9  X  r 

the  total  centrifugal  force  carried  by  a  rotor  tooth 


21.5X10 


276 


ELECTRICAL  MACHINE  DESIGN 


HIGH  SPEED  ALTERNATORS  277 

centrifugal  force 


the  stress  at  the  bottom  of  a  rotor  tooth  = 
(r^-r^r.p.m.2 


t 


(34) 


Stress  in  the  Disc. 

The  centrifugal  force  of  the  section  of  the  rotor  enclosed  in 

i     a     (r^  —  r^r.p.m.2  8  „ 
the  angle  /?  =        2LVX  iV     ~  lb" 

the  vertical  component  of  this  force 

''.p.m.^ 


21.5X10" 


Part  of  Wedse 


FIG.  192. 

the  total  vertical  component  due  to  half  the  rotor 

e 
average  value  of  sin 


21  5X106 


1.9X105 


/  /v»  3  ^_>  A»   3"\  ^»  />^  -oo^    2 

the  stress  in  the  section  dr  —  —  l 


(35) 


3.8XdrXl05 

Stress  in  the  Wedge. 

The  total  force  acting  upward  on  the  wedge  is  the  centrifugal 
force  of  the  contents  of  the  slot 


J 


=      sXdrX0.3X 


•.p.m.V 
60    / 


X 


12 

gxr 


278  ELECTRICAL  MACHINE  DESIGN 

=  (r12-r22)XsXr.p.m2 
2.3  XlO5 

=  P 

p 

the  stress  at  section  ab  due  to  shear  =  -  —  ^  =S 


the  stress  at  point  6  dud  to  bending  =  —  -r-  p  =  B 

ry  I  r>2 

the  maximum  stress  in  the  wedge  =  -^  +  \-j-  +  *S2 

206.  Diameter  of  the  Shaft.  —  Every  shaft  deflects  due  to  the 
weight  which  it  carries  so  that  as  it  revolves  it  is  bent  to  and 
fro  once  in  a  revolution.  If  the  speed  at  which  the  shaft  revolves 
is  such  that  the  frequency  of  this  bending  is  the  same  as  the 
natural  frequency  of  vibration  of  the  shaft  laterally  between  its 
bearings  then  the  equilibrium  becomes  unstable,  the  vibration 
excessive,  and  the  shaft  liable  to  break  unless  very  stiff.  The 
speed  at  which  this  takes  place  is  called  the  critical  speed  and 
should  not  be  within  20  per  cent,  of  the  actual  running  speed. 

VP   T 


where  E  =  Youngs  modulus  for  the  shaft  material 

7  =  the  moment  of  inertia  of  the  shaft  section  about  a 

diameter  =  ^rds4 

DTC 

weight  of  rotor 
M  =  the  mass  of  the  revolving  part  =  — 

2L  =  the  distance  between  the  bearings,  see  Fig.  191 
Hhe  const  ant  =  75  for  turbo  rotors  if  inch  and  Ib.  units  are  used 

/  28  X  106 

therefore  the  critical  speed  =  100  Xds2\-         '    .  ,.    —^       (36) 

^  rotor  weight  XL3 

If,  instead  of  vibrating  as  a  whole,  the  shaft  vibrates  in  two 
halves  with  a  node  in  the  middle,  then  the  frequency  of  this 
harmonic  is  got  by  substituting  for  L  in  the  above  equation  the 
value  Z//2  and  is  equal  to 

=  the  fundamental  frequency  X23  ;  2 

=  2.8  times  the  fundamental  frequency. 

It  is  found  in  practice  that  this   harmonic  has  a  value  which 
varies  from  about  2.4  to  2.6  times  the  fundamental  frequency. 

The  deflection  of  the  shaft  is  generally  limited  to  5  per  cent. 

1  Behrend,  Elect.  Rev.,  N.  Y.,  1904,  page  375. 


HIGH  SPEED  ALTERNATORS  279 

of  the  air-gap  clearance  so  that  'there  shall  not  be  any  trouble 
due  to  magnetic  unbalancing,  therefore 


TFv 
deflection--  ~~  =  0.05d  inches 


where  TF  =  the  weight  of  the  rotor  +  the  unbalanced  magnetic 
pull  inlb.;  see  Art.  346. 

The  stress  in  the  shaft  is  determined  as  follows: 

WL. 

Mb,  the  bending  moment  at  the  center  of  the  shaft  =  —  ^pinch  Ib. 

z/ 

watts  input        33000 

Mt,  the  twisting  moment  =  --  ,_.,       —  Xx—        —  Xl2 

74o  2;rr.p.m. 

watts  input       r  .     ,   .. 

-X  85  inch  Ib. 
r.p.nr 


•     i     x  u     ,r 

Me,  the  equivalent  bending  moment  = 


=  stress  Xds3  (37) 

Oa 

207.  Heating  of  Turbo  Rotors.  —  The  assumption  made  in  the 
following  discussion  is  that  all  the  heat  generated  in  the  part 
abed  of  the  rotor,  Fig.  191,  is  dissipated  from  the  surface  nDrl, 
so  that  each  part  of  the  rotor  gets  rid  of  its  own  heat  and  there 
is  no  conduction  axially  along  the  winding. 

The  difference  in  temperature  between  the  rotor  copper  and 
the  air  which  enters  the  machine 

—  the  difference  in  temperature  from  copper  to  iron 

+  the  difference  in  temperature  between  the  iron  and  the  air 

at  the  rotor  surface 

+  the  difference  in  temperature  between  the  air  at  the  rotor 
surface  and  that  entering  the  machine,  which  value  may  be 
taken  as  15°  C. 

It  was  shown  in  Art.  94,  page  109,  that  in  any  slot  the  difference 
in  temperature  between  the  copper  and  the  iron 

_amp.  cond.  per  slot     thickness  of  insulation        1 
cir.  mils  per  amp.  2d  +  s  0.003 

amp.  cond.  per  pole  X  33  1 

X 


slots  per  poleX  cir  mils  per  amp.  (2d) 
taking  the  thickness  of  slot  insulation  and  the  slot  clearance  to  be 
0.1  in.  and  neglecting  s  for  the  case  of  strip  copper  laid  flat  in 
the  slot,  because  the  heat  will  not  travel  down  through  the 
layers  of  insulation. 


280  ELECTRICAL  MACHINE  DESIGN 

The  difference  in  temperature  between  the  rotor  surface  and 
the  air  surrounding  it  is  found  as  follows  : 
The  resistance  of  a  conductor  of  M  cir.  mils  section,  I  in.  long 

=sohm- 

II  2 
The  loss  in  this  conductor  =^-  watts. 

M 


The  total  loss  in  section  abcd  =  —^r-  cond.  per  slot  X  slots  per 

amp.  cond.  per  pole 

poleXpoles.  =  —  ^-  —  -^—  -XpXl 

cir.  mils  per  amp. 

The  watts  per  square  inch  of  radiating  surface 
_amp.  cond.  per  pole     pXl 

cir.  mils  per  amp.       xDrl 
_  amp.  cond.  per  pole     1 

cir.  mils  per  amp.      r  ' 

The  temperature  rise  of  this  surface  above  that  of  the  air 
which  surrounds  it  is  10°  C.  per  watt  per  square  inch  when  the 
peripheral  velocity  is  20,000  ft.  per  minute.  This  is  a  lower  value 
than  that  which  would  have  been  obtained  by  the  use  of  the 
curves  in  Fig.  177,  page  239,  but  these  curves  were  based  on 
the  results  obtained  from  tests  on  definite  pole  machines  which 
stir  up  the  air  much  better  than  does  the  cylindrical  type  of 
rotor,  and  further,  the  radiating  surface  was  assumed  to  be  the 
external  surface  of  the  coils,  whereas  it  should  include  the  surface 
of  the  poles  and  field  ring  to  be  on  the  same  basis  as  the  above 
figure  for  cylindrical  rotors. 

The  temperature  rise  of  the  rotor  surface  above  that  of  the 
surrounding  air  is  therefore 

_  amp.  cond.  per  pole  10 

cir.  mils  per  amp.      pole-pitch* 

The  temperature  rise  of  the  rotor  copper  above  that  of  the 
air  entering  the  power-house  in  °C 
_  amp.  cond.  per  pole/        10  33  ^     i  * 

cir.  mils  per  amp.    ypole-pitch     slots  per  pole  (2d)/ 
and  for  a  temperature  rise  of  100°  C. 
cir.  mils  per  amp.  = 

amp.  cond.  per  pole/        10  33  \     ,„„, 

85  ~\  pole-pitch  +  slots  per  pole  (2d))"  (     ' 


HIGH  SPEED  ALTERNATORS  281 

208.  Heating  of  Turbo  Stators. — For  its  output,  the  radiating 
surface  of  a  turbo  alternator  is  generally  small,  and  it  is  advisable 
to  cool  such  machines  by  forced  ventilation.  At  present  most 
turbos  are  self-contained  and  have  fans  attached  to  the  rotor 
to  move  the  necessary  volume  of  air;  these  fans  are  very  ineffi- 
cient, and,  in  passing  through  them,  the  air  is  heated  and  raised 
in  temperature  from  5  to  10°  C.  In  the  machine  shown  in 
Fig.  191  the  air  is  supplied  by  an  external  fan  and  is  filtered 
before  it  enters  the  generator. 

If,    in    a    machine   which    is    cooled    by   forced    ventilation, 
ti=  the  temperature  of  the  air  at  the  inlet  in  deg.  C., 
£0=the  average  temperature  of  the  air  at  the  outlet  in  deg.  C., 
then  each  pound  of  air  passing  through  the  machine  per  minute 
takes  with  it  0.238(£0  —  tj)  Ib.  calories  per  minute 

or  7.5(£0  —ti)  watts 

and  each  cubic  foot  of  air  per  minute  takes 
0.53600-^)  watts 

since  the  specific  heat  of  air  at  constant  pressure  =  0.238  and 
the  volume  of  1  Ib.  of  air  is  approximately  14  cu.  ft. 

If  100  cu.  ft.  of  air  per  minute  are  supplied  for  each  kilowatt 
loss  in  the  machine  then  the  average  rise  in  temperature  of  the 
air  will  be  19°  C. 

When  air  is  blown  across  the  surface  of  an  iron  core  at  V  ft 
per   minute   the   watts   dissipated   per   square   inch   for    1°   C 
rise  of  the  surface  =  0.0245(1 +0.00127  V).     It  is  not  generally 
advisable  to  use  velocities  higher   than  6000   ft.    per   minute, 
because  for  higher  velocities  the  air  friction  loss  is  large  and  the 
air  is  heated  up  due  to  this  loss.     For  this  air  velocity  the  watts 
per  square  inch  for  1°  C.  rise  =  0.21. 

The  watts  per  square  inch  of  vent  duct  surface 

=  watts  per  cubic  inchX^,  Fig.  82,  page  104, 
where  .XT  =  half  the  distance  between  vent  ducts. 

For  2-in.  blocks  of  iron,  a  velocity  of  6000  ft.  per  minute  and 
a  difference  in  temperature  between  the  iron  and  the  air  of 
10°  C. 

watts  per  cubic  inch  =0.21  X 10 

=  2.1 

and  the  watts  per  pound  =  7. 5  which,  as  may  be  seen  from  Fig. 
81,  page  102,  corresponds  to  a  value  of  flux  density  of 


282  ELECTRICAL  MACHINE  DESIGN 

75,000  lines  per  square  inch  at  60  cycles 
and       120,000  lines  per  square  inch  at  25  cycles. 
As  a  matter  of  fact  the  iron  loss  in  turbo  generators  is  about 
0.7  times  the  value  found  from  the  curves  in  Fig.  81  because  the 
bulk  of  this  loss  is  in  the  core  behind  the  teeth  and  is  therefore  not 
affected  by  filing  of  the  slots;  the  pole  face  loss  in  a  turbo  generator 
is  also  small  because  the  air  gap  is  long  and  so  prevents  tufting 
of  the  flux. 

In  a  long  machine  like  a  turbo  generator  most  of  the  heat  due 
to  stator  copper  loss  has  to  be  conducted  through  the  slot  in- 
sulation and  dissipated  from  the  sides  of  the  vent  ducts,  and  this 
counteracts  the  effect  of  the  reduced  core  loss  so  far  as  core 
heating  is  concerned.  For  a  new  machine  the  following  values 
of  flux  density  should  not  be  exceeded  unless  there  is  considerable 
information  obtained  from  tests  on  other  machines  which  would 
justify  the  use  of  higher  values. 

Maximum  tooth  Maximum  core 

Frequency  density,  lines  per  density,  lines  per 

square  inch  square  inch 

25  cycles 120,000  85,000 

60  cycles 100,000  65,000 

for  ordinary  iron  0.014  in.  thick. 

209.  Short-circuits. — When  an  alternator  running  at  normal 
speed  is  short-circuited  and  the  field  excitation  gradually 
increased,  the  current  which  flows  for  any  field  excitation  can  be 
found  from  a  short-circuit  curve  such  as  that  in  Fig.  167,  page 
225,  and  at  the  excitation  for  normal  voltage  and  no-load  the 
armature  current  on  short-circuit  will  seldom  exceed  three  times 
full-load  current. 

The  terminal  voltage  and  the  power  factor  are  both  zero  on 
short-circuit,  and  the  voltage  drop,  as  shown  in  diagram  A,  Fig. 
193,  is  made  up  of  the  drop  E0Eg  due  to  armature  reaction,  and 
of  the  armature  reactance  drop  IX. 

When  an  alternator,  running  at  normal  speed,  no-load  and 
excited  for  normal  voltage,  is  suddenly  short-circuited,  the  arma- 
ture current  increases  and  tends  to  demagnetize  the  poles.  Now 
the  flux  in  the  poles  cannot  change  suddenly  because  the  poles  are 
surrounded  by  the  field  coils,  which  are  short-circuited  through 
the  exciter,  so  that  any  decrease  in  the  flux  in  the  poles  causes  a 
current  to  flow  round  the  field  coils  in  such  a  direction  as  to 


HIGH  SPEED  ALTERNATORS 


283 


maintain  the  flux.  The  armature  reaction  is  therefore  not  instan- 
taneous in  action  and  at  the  first  instant  after  the  short-circuit  the 
current  in  the  armature  is  limited  only  by  the  armature  reactance. 
The  operation  of  an  alternator  on  a  sudden  short-circuit  is  shown 
in  diagram  B,  Fig.  193. 

The  maximum  value  of  the  current  depends  on  the  value  of 
the  voltage  at  the  instant  of  the  short-circuit;  in  Fig.  194, 
curve  1  gives  the  value  of  the  generated  e.m.f.  at  any  instant, 
and  curve  2  the  value  of  the  reactance  voltage  at  any  instant 
during  the  first  few  cycles  after  the  short-circuit;  the  terminal 
voltage  is  zero,  the  armature  reaction  is  dampened  out  by  the 
field  winding,  and  the  reactance  voltage  is  equal  and  opposite 
to  the  generated  e.m.f. 


E< 


Y/^T 

A 


'IX 


B 

FIG.  193.  —  Vector  diagram  for  an  alternator  on  short  circuit. 

The  reactance  voltage  is  produced  by  the  change  in  the  short- 
circuit  current  and,  according  to  Lenz's  law,  acts  in  such  a 
direction  as  to  oppose  this  change.  If  then,  as  in  diagram  A, 
Fig.  194,  the  short-circuit  takes  place  at  the  instant  a,  when  the 
generated  voltage  is  a  maximum,  then  between  a  and  b  the  re- 
actance voltage  is  negative  and  must  therefore  be  opposing  a 
growth  of  current  while  between  6  and  c  the  reactance  voltage 
is  positive  and  must  be  opposing  a  decay  of  current.  At  the 
instant  of  short-circuit  the  current  is  zero,  and  curve  3  is  the 
current  curve  which  meets  these  conditions. 

If,  as  in  diagram  B,  Fig.  194,  the  short-circuit  takes  place  at 
the  instant  /,  when  the  generated  voltage  is  zero,  then  between 
/  and  g  the  reactance  voltage  is  positive  and  must  therefore  be 
opposing  a  decay  of  current  while  between  g  and  h  the  reactance 


284 


ELECTRICAL  MACHINE  DESIGN 


voltage  is  negative  and  must  be  opposing  a  growth  of  current. 
At  the  instant  of  short-circuit  the  current  is  zero  and  curve  3 
is  that  current  curve  which  meets  these  conditions. 

Neglecting  the  leakage  reactance  of  the  rotor,  the  current  in 
the  case  represented  by  diagram  A;  Fig.  194,  has  an  effective 


FIG.  194. — Effect  on  the  value  of  the  current  of  the  point  of  the  e.m.f. 
wave  at  which  the  short  circuit  occurs. 

generated  voltage  per  phase 

value  =—  ,  — ,  while    in    the    case   repre- 

reactance  per  phase 

sented  by  diagram  B  the  maximum  current  is  twice  as  large. 

210.  Probable  Value  of  the  Current  on  an  Instantaneous  Short- 
circuit.^ — It  was  shown  in  the  last  article  that  the  effective  current 
under  the  most  favorable  conditions 

generated  voltage  per  phase 
=—  --,  and  therefore 

reactance  per  phase 


HIGH  SPEED  ALTERNATORS  285 

current  on  instantaneous  short-circuit  _  generated  voltage 
full-load  current  reactance   voltage* 

The  generated  voltage  per  phase 

=  2.22  X&XZ0a/10-8  formula  25,  page  190 

=  2.12(6cp)  X(B^rLc)/10-8  taking  k  =  0.96; 
the  reactance  voltage  per  phase 

=  2nfb2c2p[<j)eLe  +  ((/>s+(i>t)Lc]lO-8Xl    for   a    chain    winding; 
formula  28,  page  223. 


=  2rfb2c2p  -  +  (0s+<j^)Lc]  10~8X/   for    a    double    layer 

£ 

winding;  formula  29,  page  223 

where  —  -  varies  with  the  pole-pitch  as  shown  in  Fig.  195 

—  =  —     x-l  +  — -1 —-{ — -      and  since  cXnXs,  the  total 

n     en  [3s     s      s  +  w     w\ 

slot  width  per  pole,  is  proportional  to  the  pole-pitch, 
therefore  —  is  approximately  inversely  proportional 

IV 

to  the  pole-pitch. 

Ct 

0$=0.42  (ptp  —  1.34:^  for  machines  with  definite  pole  ro- 
tors, neglecting  the  value  of  </> ia 

Ct 
=  3.2  ^  for  machines  with  cylindrical  rotors,  the  type 

generally  used  for  turbo  generators.  In  order 
that  the  regulation  of  the  machine  may  have 
a  reasonable  value,  d,  the  air-gap,  is  fixed  by  the 
value  of  the  armature  ampere-turns  per  pole  and 
is  approximately  proportional  to  the  pole-pitch, 
therefore  <j>t  is  approximately  inversely  propor- 
tional to  the  pole-pitch. 

„,        ,.    reactance  voltage        3q  [(f)eLc     <t>s+<f>t]  f  u   • 

The  ratio-  — =%-^r  rV£  +  — -^     for   a  chain 

generated  voltage      Bg((>[nLc  n 

winding  =  -=-^-  %—£-  +  — — —  for  a  double  layer  winding, 
Bg</>  \2nLc          n      \ 

<bs+(bt     a  constant  £  .  -    ,  /on, 

where    J-?__L±  =  — _^  for  a  given  number  of  phases.      (39) 

n          pole-pitch 

The  values  of  </>s  and  (f>t  are  plotted  in  Fig.  195  for  average 
machines  which  have  not  less  than  two  slots  per  phase  per  pole 


286 


ELECTRICAL  MACHINE  DESIGN 


nor  a  larger  slot  pitch  than  2.75  in.,  and  for  machines  with  open 
slots  and  laminated  rotors. 

Example. — Determine  approximately  the  per  cent,  reactance 
drop  at  full-load  in  the  following  machine: 

Normal  output  in  k.v.a 6250 

Normal  voltage  at  terminals 2400 

Number  of  phases 3 

Current  per  phase 1500 

R.p.m 1800 

Frequency 60  cycle 

Internal  diameter  of  armature 45  in 

Pole-pitch 35.5  in. 

Frame  length 51  in. 

Average  gap  density 30,000  lines  per  square  inch 

Per  cent,  enclosure 1.0 

Ampere  conductors  per  inch 635 

Winding Double  layer,  Y-connected 


10  20  30 

Pole  Eitch  in  Inches 
Definite  Poles  Cylindrical  Rotors 

FIG.  195.— Values  of  the  leakage  fluxes. 


40 


3X635/    17 
=  30,  000 


Reactance  voltage 
Generated  voltage 

When  a  solid  pole  face  is  used,  as  in  most  turbo  alternators 
with  cylindrical  rotors,  the  value  of  <pt  will  be  lower  than  that 
found  from  Fig.  195,  because  the  flux  will  be  prevented  from 
entering  the  pole  face  by  eddy  currents  which  it  produces  therein; 
this  tends  to  make  the  short-circuit  current  larger  than  the  value 
found  from  formula  39. 

Down  to  this  point  the  effect  of  the  leakage  reactance  of  the 
rotor  winding  has  been  neglected.  As  shown  in  Fig.  159,  page 
213,  the  total  flux  per  pole  =  (f>m  =  </>0  +  (f>e  and  this  remains 
constant  during  the  first  few  cycles  after  an  instantaneous 
short-circuit.  In  order  that  (f>m  remain  constant  a  current 
must  flow  in  the  rotor  winding  in  such  a  direction  as  to  oppose 


HIGH  SPEED  ALTERNATORS  287 

the  demagnetizing  effect  of  the  armature  reaction.     This  current 

is  large,  so  that  the  m.m.f.  between  the  poles  and,  therefore, 

the  leakage  flux  (f>e  are  much  larger  immediately  after  a  sudden 

short-circuit  than  at  no-load. 

If  (j)eo=ihQ  pole  leakage  flux  at  no-load 

and  (f>es  =the  pole  leakage  flux  immediately  after  a  short-circuit, 

then  the  generated  voltage  in  the  machine,  which  is  produced 

by  the  flux  <j>a,  is  less  immediately  after  a  short-circuit  than  it 

was  immediately  before  in  the  ratio  —^ — ~1  and  this  tends 

<f>m—  <peo 

to  make  the  short-circuit  current  smaller  than  the  value  found 
from  formula  39. 

,.     current  on  instantaneous  short  circuit 
To  reduce  the  ratio  -  £  ,,  , — -t — 

full-load  current 

it  is  necessary  as  shown  in  formula  39: 

To   increase  the  value   of  q,  the  ampere  conductors  per  inch; 

this   will  at  the  same  time  cheapen  the  machine  but  will 

cause  its  regulation  to  be  poorer. 
Use  a  chain  rather  than  a  double-layer  winding  so  as  to  increase 

the  end  connection  reactance. 
Use  deep,  narrow  and  closed  slots  so  as  to  increase  the  slot 

reactance. 
Use  as  small  a  pole-pitch  as  possible  until  the  point  is  reached 

at  which  the  term  becomes  of  more  importance  than 

<£>s  +<£< 

the  term  -       — . 
n 

Use  a  laminated  rotor  if  possible. 

Use  a  cylindrical  rotor  rather  than  one  of  the  definite  pole  type, 

because  of  the  larger  value  of  (f>t,  as  may  be  seen  from  Fig.  195. 

All  the   above   changes  are   made   to  increase  the  reactance  of 

the  machine  and,  therefore,  tend  to  make  the  regulation  poor. 

The  value  of  the  instantaneous  short-circuit  current  can  be 
reduced  by  making  the  pole  leakage  factor  large  and  this  will  not 
affect  the  regulation  seriously  if  the  pole  pieces  are  unsaturated 
at  normal  voltage. 

211.  Supports  for  Stator  End  Connections. — The  large  current 
due  to  an  instantaneous  short-circuit  takes  several  seconds  to 
get  down  to  the  value  which  it  would  have  on  a  gradual  short- 
circuit,  and  during  this  time  the  force  of  attraction  between 
adjacent  conductors  of  the  same  phase  is  very  large  and  tends 


288 


ELECTRICAL  MACHINE  DESIGN 


to  bunch  the  end  connections  of  each  phase  together.  The 
force  between  the  groups  of  end  connections  of  adjacent  phases 
is  also  very  large  and,  when  the  currents  in  these  phases  are  in 
opposite  directions,  this  force  tends  to  separate  the  phase  groups 
of  end  connections.  To  prevent  any  movement  of  the  coils  due 
to  this  effect  it  is  necessary  to  brace  them  thoroughly  in  some 
such  way  as  that  shown  in  Fig.  191. 

212.  The  Gap  Density. — For  the  type  of  rotor  shown  in  Fig. 
191  the  distribution  of  flux  in  the  air  gap  is  given  by  the  heavy 
line  curve  in  Fig.  196;  if  two  more  slots  per  pole  are  added,  as 


!.  L 

-<•                      8                   v 

FIG.  196. — Flux  distribution  in  the  air  gap  of  a  turbo  alternator. 

shown  dotted  in  Fig.  196,  the  flux  will  be  increased  by  the  amount 
enclosed  by  the  dotted  curve  and,  for  a  considerable  increase  in 
rotor  copper  and  rotor  loss,  only  a  small  increase  in  the  flux  per 
pole  will  be  obtained.  The  angle  ft  is  therefore  seldom  made 
less  than  30  electrical  degrees  and  for  this  value  the  maximum 
gap  density  =  the  average  gap  density  X  1.5  approximately. 

The  maximum  gap  density  depends  on  the  peimissible  value 
of  the  maximum  tooth  density  since 


- 

*-*  g  max        J-Jtmax^j  )} 

the  blocks  of  iron  in  the  core  are  about  2  in.  thick,  the  vent 
ducts   0.625   in.   wide   and  the   stacking  factor  =  0.9, 
therefore 

^  =  0.68; 


HIGH  SPEED  ALTERNATORS  289 

an  average  value  for  -  =  1.5  for  turbos,  since  the  slot  pitch  is 

6 

generally  large 

and    Bt  max  =  100,000  lines  per  square  inch  for  60  cycles 

=  120,000  lines  per  square  inch  for  25  cycles 
therefore 

Bgmax=  45,000  lines  per  square  inch  for  60  cycles 

=  54,000  lines  per  square  inch  for  25  cycles 
213.  The  Demagnetizing  Ampere  -turns  per  Pole  at  Zero 
Power  Factor.  —  The  distribution  of  the  m.m.f.  of  armature 
reaction  at  two  different  instants  is  shown  in  Fig.  160,  page  214, 
for  a  machine  with  six  slots  per  pole  and  b  conductors  per  slot. 
In  the  case  of  a  definite  pole  machine  the  portion  of  this  diagram 
which  is  cross  hatched  is  effective  in  demagnetizing  the  poles, 
whereas  in  the  type  of  machine  with  a  cylindrical  rotor  the  whole 
armature  m.m.f.  is  effective  and  for  this  case 

A  Tav  X  6  A  =  area  of  diagram  A 


=  area  of  diagram  B 

.8666/m  X2/1 


=  6.9667OT^  the  average  value  from  diagrams  A 

and  B 
therefore  ATav  =  l.WbIm 

=  1.646/c  where  Ic  is  the  effective  current  per 
conductor 

/slots  per  poleN 


=  1.6467C  ,- 


=  0.275  Xcond.  per  poleX/c 

The  maximum  m.m.f.  of  the  field  windings  is  that  at  the  center 
of  the  poles  and  is  equal  to  the  ampere-turns  per  pole. 

The  average  m.m.f.  when  /?,  Fig.  196,  is  30  electrical  degrees 

maximum  m.m.f. 

1  K  -  approximately 

i.o 

_the  ampere-turns  per  pole 
1.5 

19 


290  ELECTRICAL  MACHINE  DESIGN 

therefore  the  ampere  turns  per  pole  required    on  the  field  to 
overcome  the  demagnetizing  effect  of  the  armature 

=  1. 5  X  0.275  X  cond.  per  poleX/c 

=  0.41  X  cond.  per  pole  X  Ic  (40) 

214.  Relation  between  the  Ampere  -turns  per  pole  on  Field  and 
Armature. — For  definite  pole  machines  the  value  of  the  ampere- 
turns  for  the  gap  on  no-load  and  normal  voltage 

=  ATg 

=  1,5  times  the  armature  ampere-turns  per  pole  for  a  first 

approximation,  see  Art.  183,  page  240. 

It  may  be  seen  by  a  comparison  of  formulae  27  and  40,  pages 
215  and  290,  that,  for  a  machine  with  a  cylindrical  rotor,  a  larger 
number  of  field  ampere-turns  are  required  to  overcome  the 
demagnetizing  effect  of  the  armature  than  for  a  definite  pole 
machine;  and  further,  it  will  be  seen  from  the  example  in  Art.  215 
that  the  air  gap  of  a  turbo  alternator  is  very  long  and  the  number 
of  ampere-turns  used  up  in  sending  the  flux  through  the  poles  is, 
therefore,  very  small  compared  with  that  required  for  the  gap,  so 
that  the  saturation  curve  does  not  bend  over  and  the  advantage  of 
a  saturated  pole,  pointed  out  in  Art.  175,  page  228,  cannot  readily 
be  obtained.  For  these  two  reasons  it  is  necessary,  in  order  to 
get  reasonably  good  regulation  from  a  turbo  alternator,  to  make 
A Tg  =  1.75  (armature  ampere-turns  per  pole  at  full-load)  for  a 

first  approximation, 

a  value  which  is  about  25  per  cent,  larger  than  for  a  definite 
pole  machine. 

215.  Procedure  in  Turbo  Design. — The  method  whereby  the 
preliminary  design  of  a  turbo  alternator  is  worked  out  can  best 
be  seen  from  the  following  example. 

Work  out  the  preliminary  design  for  a  5000  kw.  2400  volt, 
three-phase,  1500  ampere,  60  cycle,  1800  r.p.m.  machine,  to 
operate  at  80  per  cent,  power  factor. 

Maximum  peripheral  velocity,  20,000  ft.  per  minute  assumed 

Rotor  diameter,  Z)r  =  42.5in. 

Rotor  pole  pitch,  r  =  33.5  in. 

Amp.  cond.  per  inch,  q  =  600,  see  Art.  195,  page  258 

Armature  amp. -turn  per  pole,  =  —  =  10,000 

pr  .  2 

ATg  =1.75X1 0,000  for  a  first  approxi- 

mation 
=  17,500 


HIGH  SPEED  ALTERNATORS 


291 


Probable  value  of  Cd 

C  may  be  taken 

Internal  diameter  of  stator, 

Total  conductors  (probable)  , 

Pole  pitch, 

Slots  per  pole 

Total  slots 

Conductors  per  slot 

Total  conductors  (actual), 

Flux  per  pole, 

Slot  pitch, 

Slot  width, 

Tooth  width, 

Tooth  area  required  per  pole 

Net  length  of  iron  in  the  core, 
Gross  length  of  iron  in  the  core, 
Center  vent  ducts 
Frame  length, 

Average  gap  density, 


=  3.2xATg 

•t>g  max 

=  1.25.  in. 

.  =1.0  for  such  a  large  air  gap 
Z>0=45  in. 

Zc  =  qX*Da  =  57 

Ic 

r  =  35.5.  in. 
=15 
=  60 
=  1 

Zc  =  60 

<£a  =  54.5X  106 
A  =2.36  in. 
s=0.8in. 
/  =  1.56  in. 


av 


=  820sq.  in. 


1.5 

Ln  =  35  in. 
L^  =  39  in. 

=  19-0.625  in. 
Lc  =  51  in. 

av=^  =30,000    lines   per    square 
inch. 

The  machine  is  now  drawn  approximately  to  scale  and  the 
distance  between  bearings  determined;  this  distance  =140  in. 
Rotor  Design. 

=  ^X42.52X5lX0.2s)  1.5   =  30,000  lb.; 

the  multiplier   1.5  is  used  to  take  ac- 
count of  end  connections,  coil  retainers. 
etc. 
=16  in. 

the  stress  in  the  shaft  =2600  lb.  per  sq. 

in.  and 

the  shaft  deflection  =0  018  in. 

neglecting  the  unbalanced  magnetic  pull. 


Probable  rotor  weight 


Shaft  diameter 


and 
Depth  below  slots  =  d 

.  .   .     x, 

Rotor  slot  depth 


VOQ  y  1  A6 
30,000  X7Q3  formula  36> 
278 

=  1340  r.p.m. 
=  2.4  X  1340  =  3240  r.p.m. 

(21  253  _  83}18002 
=  3.8xi4;oooxiQ^  formula  35,  page  277 

=  5.5  in. 

(42.5  -16-11) 
—  •=  — 


292 


ELECTRICAL  MACHINE  DESIGN 


Probable  depth  of  wedge 

Available  slot  depth 
Armature  amp. -turns  per  pole 
Max.  field  amp.-turns  per  pole 

Probable  mean  turn 
Section  of  rotor  conductor 


Cir  mils  per  ampere 


Maximum  exciting  current 


Ampere  conductors  per  slot 


Conductors  per  slot 


=  7.75  in. 

=  1.25;  should  be  checked  after  the  slot 

width  has  been  determined 
=  6.5  in. 
=  11,250 

=  3.25X11,250  assumed 
=  37,000 
=  156  in.  from  scale  drawing 


37,000X156 


formula    7,    page    65    for 


30 

120  volt  excitation 

=  193,000;  this  value  should  be  increased 
10  per  cent,  because  of  the  high  tem- 
perature at  which  the  field  will  be  run, 
therefore, 

=  210,000  cir  mils. 

2X37,000  /  10.         33    \  formula  38, 
85        \33.5 +  6X13/     page  280 

=  640  with  6  slots  per  pole.  A  smaller 
conductor  could  be  used  if  the  rotor 
were  made  with  8  slots  per  pole  and  the 
two  rotors  should  be  worked  out 
together  to  determine  which  will  be 
the  cheaper, 
total  cir  mil  section  of  conductor 


210,000 

640 

=  328  amp. 
37,000X2 

6 
=  12,300 

12,300 
~  328  amp. 
=  38 


cir  mil  per  ampere 


The  winding  to  be  of  strip  copper  laid  flat  in  the  slot;  the 
available  depth  for  copper  and  insulation  =  6. 5,  of  which  0.2  is 
used  for  slot  insulation;  the  available  depth  for  38  conductors 
and  the  insulation  between  them  =  6. 3  in. 

=  0.15,  and  of  insulation  0.015 

=  210,000  cir  mils. 

=  0.165  sq.  in. 

=  1.1  in. 

=  1.3  in.,  allowing  0.1  in.  per  side  for  in 

sulation  and  clearance 
=  /  where 

(21.253-13.53)18002  X  360  t  +  s 

21.5X106X2^X13.5     "    X        t 
formula  34,  page  277 
=  0.65  in. 


Thickness  of  conductor 
Section  of  conductor 

Width  of  conductor 
Width  of  slot 

Width  of  tooth  at  the  root 
Tooth  stress  14,000 

From  which  t 


HIGH  SPEED  ALTERNATORS  293 

Stator  Core  Design. 

Conductors  per  slot  =  1 

Ampere  cond.  per  slot  =1500 

Ampere  cond.  per  inch  =630 

Cir  mils  per  ampere  =800;  assumed  for  a  first  approximation 

Cir  mils  per  conductor  =800X  1500 

=  1,200,000 
Section   of  conductor  =0.95  sq.  in. 

=  0.55  in.  X  1.75  in. 

=  20  strips  each  =  0.11  in.  X  0.45  in. ;  5  wide 

and  4  deep  in  the  slot. 
Slot  depth  is  found  as  follows 

0 . 45    depth  of  each  strip 
0.024  insulation  on  each  strip 

1 . 9      depth  of  conductors  and  conductor  insulation 
0. 16    depth  of  slot  insulation 
0 . 25    depth  of  wedge 
2 . 3      depth  of  slot. 
Temperature  difference  copper  to  iron 

amp.  cond.  per  slot     insul.  thickness       1       .. 
=   cir.  mils  per  amp.         2d  +  s  ~  O003  f°rmula  18'  page  U1 

_.  1500     1(0.8-0.55) 
~  800  >      ~~ 574 
=15°  C. 

This  figure  is  probably  pessimistic  because  it  neglects  the 
heat  that  is  conducted  axially  along  the  copper  and  dissipated 
at  the  end  connections,  it  also  neglects  the  effect  of  the  vent 
ducts;  it  does  indicate,  however,  that  the  section  of  copper 
chosen  is  not  too  large  because,  according  to  the  assumptions 
made  in  this  chapter, 
the  temperature  rise  of  the  air  =  19°  C.  for  100  cu.  ft.  per  minute 

per  kilowatt  loss, 
the  temperature  difference  from  stator  iron  to  air  in  ducts  =  10°  C. 

with  a  core  density  of  65,000  lines  per  square  inch, 
the  temperature  difference  from  copper  to  iron  =  15°  C. 
If  lower  temperatures  are  desired  it  is  necessary  to  use  a  larger 
supply  of  air,  lower  core  densities,  or  lower  copper  densities. 

rni_     j     xi_     e  •         u  i_-   j   xu      i  j.  flux  per  pole 

The  depth  of  iron   behind  the  slots  =  = — nr^™        ~^r- — 

2  X  65000  X  net  iron 

54000000 
"2X65000X35 
=  12  in. 

Volume  of  Air  required.     It  is  difficult  to  predetermine  the 
losses  in  a  turbo  with  any  degree  of  accuracy;  the  PR  loss  in 


294  ELECTRICAL  MACHINE  DESIGN 

the  field  and  armature  can  be  determined  accurately,  but  the 
iron  loss,  the  windage  loss  due  to  air  friction  in  the  ducts,  and 
the  load  loss  which  is  large  in  turbo  generators,  cannot  be 
determined  accurately  without  considerable  data  on  machines 
previously  built  and  tested.  For  preliminary  design-work 
Fig.  208,  page  318,  may  be  used,  which  shows  that  the  effi- 
ciency of  a  5000-kw.  turbo  at  1800  r.p.m.  is  approximately 
95  per  cent.,  neglecting  the  bearing  loss,  which  is  charged  to  the 
turbine;  therefore  the  loss  in  the  machine  =250  kw.  and  the 
volume  of  air  required  =25,000  cu.  ft.  per  minute. 
The  area  of  the  vent  duct  section 

=  number  of  ducts  X  duct  width  X  core  depth 
=  19  X  0.5  X 12  square  inches 
=  0.8  sq.  ft. 

the  vent  segments  are  0.625  in.  thick  but  the  available  space  for 
air  is  only  0.5  in. 

As  shown  in  Fig.    191,  there  are  ten  air  paths  through  the 
machine,  so  that  the  air  velocity 

25000 


10X0.8 
=  3200  ft.  per  minute; 

it  will  be  necessary  to'  use  a  higher  air  velocity  than  3200  ft. 
per  minute  in  order  to  cool  the  core;  this  may  be  obtained 
by  cutting  down  the  number  of  paths  through  the  machine 
without  changing  the  total  volume  of  air  but  may  be  better 
obtained  by  increasing  the  volume  of  air  passing  through  the 
machine. 

216.  Limitations  in  Design  due  to  Low  Voltage. — The  larger 
the  flux  per  pole  in  a  machine  the  smaller  the  number  of 
conductors  required  for  a  given  voltage  since 

E  =  a  constant X  Z  X  <£a  X/ 

and  for  large  low-voltage  machines  it  is  sometimes  difficult  to 
find  a  suitable  winding  without  considerable  change  in  the 
machine;  for  example,  in  the  turbo  designed  in  the  last  article: 
For  2400  volts,  three  phase,  the  winding  has  60  conductors, 

60  slots  and  1  conductor  per  slot  Y-connected. 
For  600  volts,   three   phase,  the  same  punching  may  be  used 

with  1  conductor  per  slot  connected  YYYY. 


HIGH  SPEED  ALTERNATORS  295 

For  500  volts,  three  phase,  a  total  of  12.5  conductors  are  required 
in  series  and  a  new  punching  is  needed  with  48  slots,  1 
conductor  per  slot  connected  YYYY. 

217.  Single-phase  Turbo  Generators. — In  the  design  of  this  type 
of  machine  a  new  difficulty  presents  itself.  It  was  shown  in 
Art  177,  page  231,  that  the  armature  reaction  in  a  single-phase 
alternator  is  pulsating  and  causes  a  double  frequency  pulsation 
of  flux  in  the  poles,  and,  therefore,  a  large  eddy  current  and 
hysteresis  loss  therein. 

These  pulsations  are  dampened  out  somewhat  by  the  eddy 
currents,  but  an  eddy-current  path  in  iron  is  a  high-resistance 
path  and  the  eddy-current  loss  is,  therefore,  large.  In  order 
to  dampen  out  the  flux  pulsations  with  a  minimum  loss  it  has 
been  found  necessary  to  surround  the  rotor  with  a  squirrel- 
cage  winding  of  copper  in  which  eddy  currents  will  be  induced 
tending  to  wipe  out  the  pulsating  effect  of  armature  reaction, 
and  since  the  resistance  of  this  squirrel  cage  can  be  made  low 
its  loss  can  be  small.  A  suitable  squirrel  cage  may  be  made 
by  using  copper  for  the  slot  wedges  shown  in  Fig.  192,  dove- 
tailing similar  wedges  into  the  pole  face,  and  connecting  them 
all  together  at  the  ends  by  copper  rings. 

The  following  figures1  show  how  necessary  these  dampers  are: 
A  1000-k.v.a.,  2-pole,  25-cycle  turbo  alternator  was  tested  three- 
phase;  one  phase  was  then  opened  and  the  machine  run  with 
two  phases  in  series,  which  gave  a  single-phase  winding  with 
2/3  of  the  total  conductors,  see  Fig.  124,  page  177.  The  same 
flux  per  pole  and  the  same  current  per  conductor  were  used  in 
each  case  with  the  following  result: 

HEAT  RUNS  ON  FULL-LOAD 

Three  phase       Single  phase       Single  phase 
no  dampers        no  dampers       with  dampers 

31  122  37  Temperature  rise  in  deg.  C. 

In  the  three-phase  machine  the  armature  reaction  is  constant 
in  value  and  revolves  at  the  same  speed  and  in  the  same  direction 
as  the  poles  so  that  dampers  are  not  required. 

The  pulsating  field  of  armature  reaction,  as  pointed  out  in 
Art.  177,  page  231,  is  equivalent  to  two  revolving  fields,  one  of 
which  revolves  in  the  same  direction  and  at  the  same  speed  as 

1  Waters,  Trans,  of  Amer.  Ihst.  of  Elect.  Eng.,  Vol.  29,  page  1069. 


296  ELECTRICAL  MACHINE  DESIGN 

the  poles,  while  the  other,  which  causes  the  trouble,  revolves  at 
the  same  speed  but  in  the  opposite  direction.  The  e.m.f. 
induced  in  an  eddy-current  path  depends  on  the  rate  at  which  the 
lines  of  force  of  this  latter  field  are  cut  and  has  a  large  value  in  a 
high-speed  turbo  alternator  but  causes  little  trouble  in  moderate- 
speed  machines. 


CHAPTER  XXVI 
SPECIAL  PROBLEMS  ON  ALTERNATORS 

218.  Flywheel  Design  for  Engine-driven  Alternators.— W  hen  two 

alternators  are  operating  properly  in  parallel  the  currents  flow 
as  shown  in  diagram  A,  Fig.  197,  and  the  operation  is  represented 
by  diagram  B.  The  e.m.fs.  P  and  Q  are  equal  and  opposite  with 
respect  to  the  closed  circuit  consisting  of  the  two  armatures 
and  the  lines  connecting  them,  and  there  is,  therefore,  no  current 
circulating  between  the  machines. 

Should  one  of  the  machines,  say  Q,  slow  down  for  an  instant  the 
currents  will  flow  as  shown  in  diagram  C,  and  the  operation  is 
represented  by  diagram  D  when  machine  Q  lags  behind  machine 
P  by  0  electrical  degrees.  The  two  e.m.fs.  are  no  longer  opposed 
to  one  another  and  there  is  a  resultant  e.m.f.  Er  which  sends  a 
circulating  current  round  the  closed  circuit.  While  this  cir- 
culating current  has  no  separate  existence,  because  it  combines 
with  the  current  which  each  machine  supplies  to  the  load  to 
give  the  resultant  current  in  the  machine,  yet  it  is  convenient  to 
consider  its  effect  separately. 

ET 

This  circulating  current  == — ^=-  and  lags  Er  by  90°, 

Xp+Xg 

where  Xp=the  synchronous  reactance  of  machine  P 
Xq=the  synchronous  reactance  of  machine  Q; 

the  resistances  of  the  armatures  and  the  resistance  and  reactance 
of  the  line  are  all  small  compared  with  the  above  reactances  and 
so  can  be  neglected.  It  may  be  seen  from  diagram  C  that  this 
circulating  current  is  in  the  same  direction  as  the  e.m.f.  in  P, 
it  therefore  acts  as  an  additional  load  on  that  machine  and  causes 
it  to  slow  down;  being  opposed  to  the  e.m.f.  in  Q  it,  therefore, 
lightens  the  load  on  that  machine  and  causes  it  to  speed  up; 
therefore,  the  two  machines  tend  to  come  together,  until  they 
are  in  the  position  shown  in  diagram  B,  where  the  machines  are 
in  step  and  the  circulating  current  is  zero.  Due,  however,  to 

297 


298 


ELECTRICAL  MACHINE  DESIGN 


the  inertia  of  the  machines,  they  will  swing  beyond  the  position 
of  no  circulating  current  which  current  will  then  be  reversed  and 
tend  to  pull  the  machines  together  again.  The  frequency  of  this 
swinging  will  be  that  of  the  natural  vibration  of  the  machines; 
the  swinging  will  gradually  die  down  due  to  the  dampening  effect 
of  eddy  currents  in  the  pole  faces,  field  coils  and  dampers. 


w 


W 


c  *    D 

FIG.  197. — Diagrammatic  representation  of  two  alternators  in  parallel. 

If  one  of  the  machines  is  direct-connected  to  an  engine  whose 
torque  is  pulsating,  forced  oscillations  will  be  impressed  on  the 
machine;  if  their  period  of  vibration  is  within  20  per  cent,  of 
the  natural  period  of  vibration,  cumulative  oscillation  will  take 
place  and  the  machines  be  thrown  out  of  step  unless  they  are 
powerfully  dampened.  It  is,  therefore,  of  extreme  importance 
to  study  the  natural  period  of  vibration  of  alternators. 

219.  Two  Like  Machines  Equally  Excited. — When  swinging 
takes  place  between  two  such  machines  they  move  in  opposite 
directions  with  the  same  frequency,  so  that  if  Fig.  198  shows  the 
vector  diagram  of  the  two  machines  referred  to  the  closed  circuit, 
then 


SPECIAL  PROBLEMS  ON  ALTERNATORS        299 

6  =  the  angle  of  displacement  between  the  two  machines; 
r\ 

a.  —  ™=the  angle  of  displacement  of  one  machine  from  the 

2j 

position  of  zero  circulating  current  or  mean  position. 

n 

Er=2E  sin- 

TyT 

I,  the  circulating  current  =  -=^  where  X  is  the  synchronous 

2X 

reactance  of  each  machine 

~ 

A 


=  I 


where  Isc  is  the  short-circuit  current  at  the  excitation  required  at 
no-load  for  voltage  E  and  may  be  found  from  a  short-circuit 
curve  such  as  that  in  Fig.  200.  Isc  is  generally  about  2.5  times 
full-load  current. 


FIG.  198. — Vector  diagram  for  two  like  machines  in  parallel. 

The  synchronising  power,  or  power  transferred  from  one  machine 
to  the  other,  in  watts 
6 


=  nEI  cos 


=  nE(I8C  sin 
sin  0 


.    0\      e 

m  TT  1  cos 

2 1        L 


300  ELECTRICAL  MACHINE  DESIGN 

r\ 

=  nEIsc  —  for  small  oscillations,  where  6  is  the  angular  dis- 
placement between  the  machines  in  electrical  radians; 

=  nEIsc  a  where  a  is  the  angular  displacement  of  one  ma- 
chine from  its  mean  position  in  electrical  radians; 

7) 

=  nEIsc  a    (-  where   a    is  the    same  angular  displacement 

a 

in  mechanical  radians. 
The  torque  corresponding  to  the  above  power  transfer 

_  lb.  at  !  ft.  radius 


=  nEIsc  — ^— X  3. 5  a 
r.p.m. 

=  Ka 

that  is  to  say,  the  torque  is  directly  proportional  to  the  displace- 
ment and  therefore  the  equation  for  the  small  displacements  is 
Wr2  d2a 

=  ~          ^rT2~ 

from  which  the  time  of  oscillation  in  seconds 

=  2.T, 


TFr2X  r.p.m. 


watts  XA^XpX  2.9 

where      TFr2=the  moment  of  inertia  of  one  machine  in  lb.  ft.2, 
r.p.m.  =the   speed    of   the    machine   in   revolutions    per 

minute, 

watts  =  the  normal  output  of  the  machine  at  unity  power 
factor, 

,.     short-circuit  current  .,    ,. 

k<=the  ratio  — c-^r  -  at  the    excitation 

full-load  current 

corresponding  to  voltage  E  at  no-load, 
p  =  ih.Q  number  of  poles. 
220.  One  Small  Machine  in  Parallel  with  Several  Large  Units.— 

In  this  case,  if  the  small  machine  is  driven  by  an  engine,  it  will 
swing  about  its  mean  position  but  will  not  be  able  to  make  the 
large  units  with  which  it  is  in  parallel  swing  in  the  opposite 


SPECIAL  PROBLEMS  ON  ALTERNATORS       301 

direction,  so  that  if  Fig.  199  shows  the  vector  diagram  of  the 
two  machines  referred  to  the  closed  circuit  then 

a=the  angle  of  displacement  between  the  small  machine  and 
the  others  with  which  it  is  in  parallel,  and  is  also  the  angle 
of  displacement  of  the  small  machine  from  its  mean  position 

Er=2Esm~ 

I,    the  circulating  current  =  -^  where   X  is   the    synchronous 

X 

reactance  of  the  small  machine;  the  reactance  of  all  the  other 
machines  in  parallel  is  very  small  compared  with  this  value 
and  may  be  neglected, 

_a  E 

sin  2  A     / 

/"' 
a  I 

=  21  sc  sin  ~2 

the  synchronising  power  in  watts 

a 
=  nEI  cos  -^ 

=  nEx2Isc  sin  ^  cos  ~ 


2 

=  n]EI8Ca 

this  is  the  same  value  as  that  obtained  for  FIG.    199. — Vector 

two  like  machines  so  that  the  time  of  oscilla-  diagram  for  a  small 

tion    will    be    the    same    as    for  two  like   machine    in    Parallel 
.  .  with   a  large  station, 

machines. 

Example.1 — Cross  compound  engines  running  at  83  revolutions 
per  minute,  with  a  flywheel  effect  of  8.5X106  Ib.  ft.2,  driving 
three-phase  alternators  of  2100  k.v.a.  output  at  50  cycles,  were 
found  to  hunt  with  the  periodicity  of  the  revolution.  The  short- 
circuit  current  of  the  machine  for  different  excitations  varied 
between  2.3  and  3.3  times  full-load  current. 

In  such  a  case  there  is  an  impulse  impressed  on  the  system 
every  stroke  or  four  impulses  per  revolution;  if  any  one  of  these 
impulses  differs  in  magnitude  from  the  others,  due  to  unequal 
steam  distribution,  there  will  also  be  a  forced  oscillation  with  the 
periodicity  of  the  revolution. 

1  Rosenberg,  Journal  of  the  Inst.  of  Elect.  Eng.,  Vol.  42,  page  549. 


302 


ELECTRICAL  MACHINE  DESIGN 


For  the  machine  in  question  the  time  of  one  cycle  of  natural 

J8.5X  106"X83~ 
acy     ^2100  X  1000X  [2.31  X  72  poles X  2.9 

L3.3J 
=  0.7  to  0.84  seconds. 

The  number  of  forced  oscillations  per  minute  due  to  unequal 
steam  distribution  is  83  and  the  corresponding  period  of 
vibration  is,  therefore,  =ff  =  0.72  seconds,  which  corresponds 
very  closely  with  that  of  the  natural  frequency.  It  was  found 
possible  to  maintain  parallel  operation  long  enough  to  allow  tests 
to  be  made  by  carefully  equalizing  the  steam  distribution  so  as 
to  eliminate  this  low  frequency  forced  oscillation. 


/  9 

Excitation 

FIG.  200. — Variation  of  the  natural  frequency  of  oscillation  with  excitation. 

It  is  advisable  to  design  the  flywheel  so  that  the  natural 
frequency  of  vibration  of  the  machine  is  lower  than  that  of  the 
lowest  forced  oscillation;  this  will  sometimes  require  the  use 
of  an  enormous  wheel;  as,  for  example,  in  the  case  of  alternators 
operating  in  parallel"  and  driven  by  large  slow-speed  gas  engines. 
Gas  engines  are  generally  of  the  four-cycle  type;  that  is,  there 
is  an  explosion  once  in  two  revolutions.  If  the  engine  is  of  the 
four-cycle,  double-acting,  cross-tandem  type  there  are  four 
explosions  to  the  revolution  and  the  forced  frequencies  in  such  a 
case  are: 


SPECIAL  PROBLEMS  ON  ALTERNATORS       303 


One  impulse  every  two  revolutions  due  to  an  unequal  distribution 

of  gas  making  one  explosion  always  more  powerful   than 

the  others;  this  is  not  a  desirable  condition  of  operation  but 

one  that  must  be  provided  for. 

One  impulse  per  revolution  due  to  the  want  of  perfect  balance 

of  the  reciprocating  parts. 
One  impulse  per  quarter  revolution  due  to  the  four  explosions  in 

each  revolution. 

In  order  that  the  natural  frequency  of  oscillation  of  the 
alternator  be  below  the  frequency  of  the  lowest  impulse  a  very 
heavy  and  expensive  flywheel  is  required,  so  that  the  wheel  is 
often  made  with  a  moment  of  inertia  of  such  a  value  that,  over 
the  whole  range  of  operation,  the  natural  frequency  of  the  alter- 
nator is  more  than  20  per  cent,  higher  than  that  of  the  lowest 
impulse  and  more  than  20  per  cent,  lower  than  that  of  the 
impulse  of  next  higher  frequency.  For  example,  in  Fig.  200 
the  excitation  during  operation  may  vary  from  of  to  og  and 
the  value  of  the  short-circuit  current  from  It  to  72.  The  natural 
frequency  of  oscillation  is  directly  proportional  to  the  square 
root  of  the  short-circuit  current,  and  for  the  value  of  W2r  chosen 
is  not  within  20  per  cent,  of  the  frequency  of  either  of  the  two 
lowest  impulses  for  any  excitation  between  of  and  og. 

221.  Use    of    Dampers. — For    gas-engine    driven    alternators 


m End  Ring. 


—  Cast  Steel 
End  Plate. 

—  Laminations. 


FIG.  201. — Alternator  dampers. 

powerful  dampers  are  supplied  because  the  applied  torque 
varies  so  much  during  each  revolution.  The  type  of  damper 
shown  in  Fig.  201  is  that  generally  used,  it  consists  of  a  complete 
squirrel  cage  around  the  machine  and  acts  as  follows: 

The  damper  rods  are  embedded  in  the  pole  face  and  so  do  not 
cut  the  main  field,  therefore  any  damping  effect  is  due  to  cut- 
ting of  the  armature  field.  If  the  armature  field  revolves  at 
synchronous  speed  with  a  uniform  angular  velocity  then,  due  to 


304 


ELECTRICAL  MACHINE  DESIGN 


the  impulses  of  the  engine,  the  poles  oscillate  about  the  position 
of  uniform  angular  velocity  and  cut  this  field.  The  curve  in 
Fig.  202  shows  the  distribution  of  the  armature  field;  the  poles 
move  relative  to  it  in  the  direction  of  the  arrow  and  e.m.fs.  are 
induced  in  the  rotor  bars  in  the  direction  shown  by  the  dots 
and  crosses.  The  frequency  of  these  e.m.fs.  is  that  of  the 
oscillation  of  the  machine  and  is  of  the  order  of  two  cycles  per 
second,  so  that  the  reactance  of  the  damper  bars  can  be  neglected 
compared  with  their  resistance  if  the  slots  in  which  they  lie  are 
open  at  the  top  as  shown  in  Fig.  201.  The  currents  in  the  bars 
are,  therefore,  in  phase  with  the  e.m.fs.  and  so  are  also  represented 
by  the  same  crosses  and  dots;  it  may  be  seen  that  the  direction 


Damper  Torque  DamPer  Tor1ue 

FIG.  202.  —  Operation  of  dampers. 

of  these  currents  is  such  that  the  force  exerted  on  them  by  the 
armature  field  tends  to  prevent  the  relative  motion  of  the  arma- 
ture and  the  damper  rods. 

The  e.m.f.  in  a  damper  rod  at  any  instant  =  B  gaXLcXVc  X 
10~8  volts. 
Where     Bga  =  the  gap  density  at  that  part  of  the  field  which  is 

being  cut  at  the  particular  instant 
Lc=the  frame  length 

yc=the  velocity  of  the  damper   rod  relative  to  the 
armature  field  in  inches  per  second. 

„  ,,      displacement  from  mean  position 
the  average  value  of  Vc  =  time  of  l/^ 


- 
180 

where  /?  =  the  maximum  displacement  of  the  poles,  in  electrical 
degrees,  from  the  position  of  uniform  angular  velocity 
and    /n=the  frequency  of  oscillation; 
therefore  the  effective  voltage  in  a  damper  rod  is  approximately 


=  l.lXBaxLcX 


ga 


volts. 


SPECIAL  PROBLEMS  ON  ALTERNATORS        305 

The  resistance  of  a  damper  rod  of  copper  =  -—  ohms 
the  effective  current  in  a  damper  rod 

=  BgaX  ^TX4.4/nXMXlO-8 

the  current  density  in  circular  mils  per  ampere 

108X180 


The  dampening  effect  depends  on  the  value  of  the  total 
damper  current,  which,  for  a  given  machine,  depends  on  the 
number  of  damper  rods  and  on  their  section.  If  the  section  of 
these  rods  be  increased  they  will  carry  a  larger  current,  will 
have  a  greater  dampening  effect  and  the  angle  of  swing  will  be 
reduced  so  that  the  larger  this  section  the  lower  the  current 
density  because  of  the  reduction  in  the  value  of  /?. 

It  is  of  interest  to  know  the  order  of  magnitude  of  this  current 
density;  for  example,  assume  that 
J30a=25;000  lines  per  square  inch 

/?=  +  5  electrical  degrees  which  will  give  a  circulating  cur- 
rent of  about  25  per  cent,  of  full-load  current 

T=10   in.,  for  which  the  peripheral  velocity  is  6000  ft.  per 
minute  at  60  cycles 

/n  =  two  cycles  per  second. 

,  ,       .,  10SX180 

then  the  current  density  =  25;0oox5x  iox4.4x2 

=  1640  circular  mils  per  ampere. 

This  value  is  pessimistic  in  that  it  neglects  the  resistance  of  the 
end  connectors. 

It  was  pointed  out  above  that  the  dampening  effect  depends 
on  the  total  damper  section.  For  gas-engine  alternators  it  is 
usual  to  put  into  the  dampers  about  25  per  cent,  of  the  section 
of  copper  that  is  put  into  the  stator  and  then,  if  the  damping  is 
not  sufficient,  or  if  the  dampers  get  too  hot,  to  look  for  the  cause 
of  the  trouble  in  the  governor,  flywheel,  or  load  on  the  system;  a 
pulsating  load  is  equivalent  as  far  as  hunting  is  concerned  to  a 
pulsating  torque  in  the  engine. 

One  cause  of  damper  heating  must  be  carefully  guarded 
against.  If  the  dampers  are  spaced  as  in  Fig.  203,  then,  when 
in  position  A,  the  flux  threading  between  two  adjacent  dampers 
is  large,  while  in  position  B  this  flux  is  small,  so  that  every 
time  a  stator  tooth  is  passed  the  flux  threading  between  two 
20 


306 


ELECTRICAL  MACHINE  DESIGN 


damper  rods  goes  through  one  cycle  and  the  frequency  of  the 
current  which  the  induced  e.m.f.  sends  round  the  closed  circuit 
=  the  number  of  stator  slots  X  the  revolutions  per  second.  This 
current  is  not  a  damping  current  and  is  liable  to  cause  excessive 
heating  and,  to  prevent  the  flux  pulsation  which  produces  it,  the 
distance  between  damper  rods  should  be  a  multiple  of  the  stator 
slot  pitch,  as  shown  at  C. 

For  steam-engine  driven  alternators  the  strong  damping  effect 
of  the  squirrel  cage  is  seldom  required  and  a  cheaper  form  of 


L 


U  L 


T 


HJ  LJ 


O 


0    •  O 


D 


FIG.  203. — Spacing  of  dampers. 

damper  is  made  by  surrounding  the  poles  with  brass  collars 
as  shown  in  Fig.  140,  page  193,  where  the  edges  of  these  collars 
act  exactly  like  rods  threaded  across  the  pole  face  except  that 
the  effect  is  not  so  powerful,  because  they  are  shielded  by  the 
pole  tips  so  that  the  flux  cut  is  comparatively  small. 

222.  Synchronous  Motors  for  Power-factor  Correction. — Con- 
sider a  synchronous  motor  running  with  constant  load  and 
constant  applied  voltage.  If  the  field  excitation  of  the  motor  be 
increased  its  back  e.m.f.  tends  to  increase,  but  this  cannot  increase 
much  because  the  applied  voltage  is  constant  so  that  a  demagnetiz- 
ing current  must  flow  in  the  motor  armature  to  counteract  the 
effect  of  the  increased  field  excitation;  this  current  must  be 
wattless  because  the  load  is  constant  and  to  be  demagnetizing 


SPECIAL  PROBLEMS  ON  ALTERNATORS       307 

it  must  lag  the  back  generated  e.m.f.  of  the  motor  and,  there- 
fore, lead  the  applied  e.m.f.  of  the  generator. 

If  on  the  other  hand,  the  field  excitation  of  the  motor  be 
decreased  its  back  e.m.f.  tends  to  diminish  and  a  wattless  and 
magnetizing  current  must  flow  in  the  motor  armature;  to  be 
magnetizing  this  current  must  lead  the  back  generated  e.m.f. 
of  the  motor  and,  therefore,  lag  the  applied  e.m.f.  of  the  generator. 

The  size  of  motor  required  for  a  given  power-factor  correction 
may  be  found  from  a  diagram  such  as  Fig.  204  where  E  is  the 
voltage  of  the  power  station  7,  the  total  station  current  per 
phase,  lags  E  by  6  degrees,  and  the  power  factor  is  70  per  cent. 


E 


Percent  Power  Factor 
100  95       90  80  70 


FIG.  204. — Size  of  motor  for 
power  factor  correction. 


FIG.  205. — Size  of  motor  for 
power  factor  correction. 


To  raise  the  power  factor  of  this  station  to   100  per  cent, 
the  synchronous  motor  must  draw  a  leading  current  =ab  and 

nxExab  .  .,   ,, 

the   motor  input   must  be=      .innri —  k.v.a.   if  the   motor  is 

jLUUU 

running  light  and  the  efficiency  is  100  per  cent. 

It  may  be  seen  from  Fig.  204  that  to  raise  the  power  factor 

of  the  system  from 

70  to  80  per  cent,  requires  a  wattless  current  ac  per  phase, 
70  to  90  per  cent,  requires  a  wattless  current  ae  per  phase, 
70  to  95  per  cent,  requires  a  wattless  current  af  per  phase, 
70  to  100  per  cent,  requires  a  wattless  current  ab  per  phase. 


308  ELECTRICAL  MACHINE  DESIGN 

The  improvement  in  power  factor  from  95  to  100  per  cent,  is, 
therefore,  obtained  at  a  considerable  cost. 

When  synchronous  motors  are  used  for  power-factor  correction 
it  is  advisable  to  arrange  that  some  of  the  load  on  the  system 
is  carried  by  these  machines;  for  example,  if  ab,  Fig.  205,  is 
the  wattless  current  per  phase  required  for  power  factor  correc- 
tion, then  in  order  to  carry  a  mechanical  load  of  the  same  value 
in  k.v.a.  the  rating  of  the  motor  would  not  be  doubled  but 
increased  by  only  41  per  cent.;  or  for  the  case  shown  by  triangle 
abd,  with  an  increase  in  current  of  12  per  cent,  over  the  value 
required  for  the  mechanical  load  a  power-factor  correction  effect 
of  50  per  cent,  may  be  obtained. 

223.  Design  of  Synchronous  Motors. — Diagram  A,  Fig.  206, 
shows  some  of  the  saturation  curves  of  an  alternator  taken  at 
constant  current  and  varying  power  factor.     If  this  machine 
were  used  as  a  synchronous  motor  then 
for    the    maximum    power-factor,  correction  effect    the    power 

factor  of  the  motor  would  be  zero  and  the  excitation  =  o/ 
for  zero  power-factor  correction  effect  the  power  factor  of  the 

motor  would  be  100  per  cent,  and  the  excitation  =  og 
for  80  per  cent,  load  and  60  per  cent,  power-factor  correction 

effect  the  excitation  would  be  =  oh. 

Synchronous  motors  are  generally  high-speed  machines  and 
have,  therefore,  few  poles,  so  that,  as  pointed  out  in  Art.  195, 
page  258,  they  will  be  troubled  with  field  heating  if  designed 
in  the  same  way  as  synchronous  generators,  because  for  power- 
factor  correction  work  they  are  operated  with  large  excita- 
tion. In  a  synchronous  motor,  however,  close  regulation  is 
not  required  so  that  for  these  machines  the  value  of  q,  the 
ampere  conductors  per  inch,  may  be  run  about  20  per  cent, 
higher  than  the  value  given  in  Fig.  184  and  the  ratio 

maximum  field  excitation  ,  ,  .  , 

.  _  -  may  be  made  less  than  3,  which  value 

armature  AT.  per  pole 

was  suggested  as  a  first  approximation  for  synchronous  generators 
in  Art.  176,  page  229.  Diagram  B,  Fig.  206,  shows  saturation 
curves  for  a  synchronous  motor  of  the  same  rating  as  that  of 
the  generator  whose  curves  are  given  in  diagram  A. 

Since  the  flywheel  effect  of  a  synchronous  motor  is  generally 
small,  no  extra  flywheel  being  supplied,  its  natural  frequency 
of  vibration  will  generally  be  comparatively  high  and  the  machine 
therefore  liable  to  be  set  in  violent  oscillation  by  some  of  the 


SPECIAL  PROBLEMS  ON  ALTERNATORS       309 


forced  frequencies  on  the  system,  for  that  reason  synchronous 
motors  are  generally  supplied  with  dampers. 

224.  Self-starting  Synchronous  Motors.- — These  are  polyphase 
machines  which  are  used  for  motor  generator  sets  and  for  driving 


9      h 

Excitation 
A 


Excitation 

B 
FIG.  206. — Saturation  curves  of  an  alternator. 

apparatus  which  requires  a  small  starting  torque,  when  a  special 
starting  motor  is  not  desired.  They  are  built  exactly  like  gas- 
engine  alternators  and  consist  of  a  standard  synchronous  motor 
supplied  with  a  squirrel-cage  winding  on  the  poles.  The  method 
whereby  this  squirrel  cage  is  calculated  so  as  to  meet  the  required 
starting  conditions  will  be  understood  after  a  study  of  the  induc- 
tion motor;  the  following  points  of  importance,  however,  must 
be  noted  here: 

Polyphase  currents  in  the  armature  winding  produce  a  revolv- 


310 


ELECTRICAL  MACHINE  DESIGN 


ing  field  which  tends  to  pull  the  squirrel  cage  round  with  it.  In 
order  that  e.m.fs.  may  be  induced  in  the  squirrel  cage  by  the 
revolving  field  the  flux  must  enter  the  poles,  therefore  the  poles 
should  be  laminated  and,  during  the  starting  period,  the  field 
coils  should  be  open  circuited. 

The  pole  enclosure  must  be  such  that  the;  air-gap  under  the 
pole  has  a  constant  reluctance  for  all  positions  bf  the  pole  relative 
to  the  armature.  If  the  pole  were  made  as  shown  in  Fig.  207 
then  in  position  4  the  air-gap  reluctance  would  be  a  minimum 
and  in  position  B  would  be  a  maximum;  in  such  a  case  the 
machine  would  lock  in  position  A  and  would  require  a  large 
force  to  move  it  out  of  this  locking  position. 

In  Art.  283  on  the  induction  motor,  it  is  shown  that  if  the  rotor 
slot  pitch  is  a  multiple  of  that  of  the  stator,  locking  will  take 


L 


FIG.  207. — Effect  of  the  pole  arc  on  the  air  gap  reluctance. 

place  due  to  the  leakage  fields  and  that  in  order  to  prevent  this 
locking  the  rotor  slot  pitch  must  differ  from  that  of  the  stator. 
It  was  pointed  out  in  Art.  221  that  to  prevent  useless  circulating 
currents  the  rotor  slot  pitch  should  be  a  multiple  of  that  of  the 
stator,  so  that  a  compromise  must  be  made  and  the  rods  spaced 
as  shown  in  diagram  D,  Fig.  203,  where  tr,  the  rotor  tooth,  is 
made  equal  to  the  stator  slot  pitch,  for  which  value  it  will  be 
found  that  the  air-gap  reluctance  under  a  rotor  tooth,  which  is 
proportional  to  a  +  6,  is  constant  in  all  positions  of  the  rotor. 

Since  the  frequency  of  the  flux  which,  due  to  the  revolving 
field,  passes  through  the  poles,  is  very  high  at  starting,  being  equal 
to  the  frequency  of  the  applied  e.m.f.,  there  will  be  high  voltages 


SPECIAL  PROBLEMS  ON  ALTERNATORS   311 

generated  in  the  field  coils  because  the  number  of  turns  per 
coil  is  large,  so  that  for  self-starting  synchronous  motors  the 
excitation  voltage  should  be  as  low  as  possible  so  as  to  keep  down 
the  number  of  turns  per  pole  and  the  field  coils  must  be  better 
insulated  than  for  ordinary  synchronous  machines;  in  the  case 
of  machines  with  a  large  total  flux  it  is  sometimes  advisable  to 
supply  a  break-up  switch  which  will  open  up  the  field  circuit 
in  several  places  at  starting  so  that  the  starting  e.m.fs.  in  the 
different  poles  will  not  add  up.  When  the  motor  is  nearly  up 
to  speed  the  field  circuit  is  closed  and  a  small  excitation  applied 
which  tends  to  bring  the  motor  into  synchronism  and  ensures 
that  it  comes  into  step  with  the  proper  polarity. 


CHAPTER  XXVII 
SPECIFICATIONS 
225.  The  following  is  a  typical  specification  for  an  alternator. 

SPECIFICATION  FOR  AN  ALTERNATING  CURRENT  GENERATOR 
Rating. 

Rated  capacity  in  kilo  volt-amperes ....  400 

Power  factor 100  per  cent. 

Normal  terminal  voltage 2,400 

Phases 3 

Amperes  per  terminal 96 

Frequency  in  cycles  per  second 60 

Speed  in  revolutions  per  minute 600 

Construction. — The  generator  is  for  direct  connection  to  a 
horizontal  type  of  water-wheel  and  shall  be  of  the  internal 
revolving  field  type,  supplied  with  base,  two  pedestal  bearings 
bolted  to  the  base,  and  a  horizontal  shaft  extended  for  a  flange 
coupling.  The  machine  must  be  so  constructed  that  the  stator 
can  be  shifted  sideways  to  give  access  to  both  armature  and 
field  coils. 

Stator. — The  stator  coils  must  be  insulated  complete  before 
being  put  into  the  slots,  shall  be  thoroughly  impregnated  with 
compound,  and  must  be  readily  removable  for  repairs.  Shields 
must  be  supplied  to  protect  the  coils  where  they  project  beyond 
the  core. 

Bidders  must  state  the  type  of  slot  to  be  used  whether  open, 
partially  closed,  or  completely  closed. 

Rotor.- — The  rotor  must  be  strong  mechanically  and  able  to 
run  at  75  per  cent,  overspeed  with  safety.  Any  fans  or  projecting 
parts  on  the  rotor  must  be  screened  in  such  a  way  that  a  person 
working  around  the  machine  is  not  liable  to  be  hurt. 

Workmanship  and  Finish. — The  workmanship  shall  be  first 
class,  all  parts  shall  be  made  to  standard  gauge  and  interchange- 
able, and  all  surfaces  not  machined  are  to  be  dressed,  filled,  and 
rubbed  down  to  present  a  smooth  finished  appearance. 

Exciter.- — The  alternator  shall  be  separately  excited  and  the 
exciter,  which  must  be  direct-connected,  is  described  in  a  separate 
specification. 

312 


SPECIFICATIONS  313 

Rheostat. — A  suitable  field  rheostat  with  face  plate  and  sprocket 
wheel  for  distance  control  is  to  be  supplied. 

Foundation  bolts  will  not  be  furnished. 

Coupling. — This  is  to  be  supplied  by  the  builder  of  the  water- 
wheel  who  shall  send  one-half  to  the  alternator  builder  to  be 
pressed  on  the  alternator  shaft. 

General. — Bidders  shall  furnish  plans  or  cuts  with  descriptive 
matter  from  which  a  clear  idea  of  the  construction  may  be  ob- 
tained; they  shall  also  furnish  the  following  information: 
Stator  net  weight, 
Rotor  net  weight, 
Net  weight  of  base  and  pedestals, 
Shipping  weight, 

Efficiency  at  J,  J,  f ,  full-  and  1J  non-inductive  load, 
Regulation  at  normal  output,  at  100  per  cent,  and  also  at  85  per 

cent,  power  factor, 

Exciting  current,  at  normal  voltage  and  speed,  for  normal  k.v.a. 
output,  at  100  per  cent,  and  at  85  per  cent,  power  factor. 
The  exciter  voltage  is  120. 

Efficiency. — The  losses  in  the  machine  shall  be  taken  as : — 

Windage,  friction,  and  core  loss,  which  shall  be  determined  by 
driving  the  machine  by  an  independent  D.-C.  motor,  the  output 
of  which  may  be  suitably  determined,  the  alternator  being  run 
at  normal  speed  and  excited  for  normal  voltage  at  no-load. 

Field  loss,  which  shall  be  taken  as  the  exciting  current  corre- 
sponding to  the  different  loads  multiplied  by  the  corresponding 
voltage  at  the  field  terminals,  the  field  coils  being  at  their  full- 
load  temperature. 

The  armature  PR  loss;  the  armature  resistance  being  meas- 
ured immediately  after  the  full-load  heat  run. 

The  load  loss,  which  is  determined  from  a  short-circuit  core  loss 
test,  the  machine  being  short-circuited  through  an  ammeter,  run 
at  normal  speed,  and  the  field  excitation  adjusted  to  send  the 
currents  corresponding  to  the  different  loads  through  the  arma- 
ture. One-third  of  the  difference  between  the  loss  so  found  and 
the  PR  loss  for  the  same  current,  shall  be  taken  as  the  load  loss. 

Regulation. — This  shall  be  taken  as  the  per  cent,  increase  in 
terminal  voltage  when  the  load  at  which  the  guarantee  is  made 
is  reduced  to  zero,  the  speed  and  excitation  being  kept  constant. 
It  shall  be  found  by  assuming  the  synchronous  impedence 
constant  for  a  given  excitation,  this  impedence  to  be  determined 


314  ELECTRICAL  MACHINE  DESIGN 

from  saturation  curves  at  no-load  and  also  at  full-load  and  zero 
power  factor. 

Temperature. — The  machine  shall  carry  its  normal  load  in 
k.v.a.,  at  normal  voltage  and  speed  and  at  100  per  cent,  power 
factor,  continuously,  with  a  temperature  rise  that  shall  not 
exceed  40°  C.  by  thermometer  ton  any  part  of  the  machine, 
and,  immediately  after  the  full-load  heat  run,  shall  carry  25  per 
cent,  overload  for  2  hours,  at  the  same  voltage,  speed  and  power 
factor,  with  a  temperature  rise  that  shall  not  exceed  55°  C.  by 
thermometer  on  any  part  of  the  machine. 

The  temperature  rise  of  the  bearings  shall  not  exceed  40°  C. 
as  measured  by  a  thermometer  in  the  oil  well,  either  at  normal 
load  or  at  the  overload. 

No  compromise  heat  run,  other  than  one  at  normal  voltage,  zero 
power  factor,  and  with  the  armature  current  for  which  the 
guarantee  is  made,  will  be  accepted.  If  the  manufacturer  cannot 
load  the  machine,  a  heat  run  will  be  made  within  3  months  after  its 
erection  to  find  out  if  it  meets  the  heating  guarantee;  the  test 
to  be  made  by  the  alternator  builder  who  shall  supply  the 
necessary  men  and  instruments. 

Overload  Capacity. — The  machine  must  be  able  to  carry  at 
least  50  per  cent,  overload  at  80  per  cent,  power  factor  with 
the  normal  exciter  voltage  of  120. 

The  machine  shall  be  capable  of  standing  an  instantaneous 
short-circuit  when  operating  at  normal  voltage,  normal  speed, 
and  no-load,  and  must  be  able  to  carry  this  short-circuit  for 
10  seconds  without  injury. 

Insulation. — The  machine  shall  stand  the  puncture  test 
recommended  in  the  standardization  rules  of  the  American 
Institute  of  Electrical  Engineers  (latest  edition)  and  the  insula- 
tion resistance  of  the  armature  and  field  windings  shall  each 
be  greater  than  one  megohm. 

Testing  Facilities. — The  builder  shall  provide  the  necessary- 
facilities  and  labor  for  testing  the  machine  in  accordance  with 
this  specification. 

226.  Notes  on  Alternator  Specifications.  —The  builder  of  the  al- 
ternator generally  inserts  the  following  clause  in  the  specification. 

"We  guarantee  successful  parallel  operation  between  our 
generators,  without  racing,  hunting,  or  pumping,  whether  driven 
by  water-wheels  or  steam  engines,  provided  that  the  variation 
of  the  angular  velocity  of  the  prime  movers  does  not  produce 


SPECIFICATIONS  315 

between  two  generators  operating  in  parallel  a  displacement  of 
more  than  five  (5)  electrical  degrees  (2^°  on  either  side  of 
the  mean  position),  one  electrical  degree  being  equal  to  one 
mechanical  degree  divided  by  half  the  number  of  poles." 

This  clause  is  inserted  to  ensure  that  the  engine  builder  shall 
supply  such  a  flywheel  and  governor  that  the  variation  of  the 
angular  velocity  of  the  engine  during  one  revolution  shall  be 
within  reasonable  limits.  As  shown  in  Art  218,  however,  hunt- 
ing may  take  place  if  the  natural  period  of  oscillation  of  the 
machine  is  approximately  the  same  as  that  of  any  of  the  forced 
oscillations  on  the  system.  In  practically  every  case  the  burden 
of  proof  when  hunting  takes  place  is  put  on  to  the  alternator 
builder. 

In  the  case  of  alternators  for  direct  connection  to  gas  engines 
it  is  often  advisable  for  the  alternator  builder  to  check  up  the 
size  of  the  proposed  flywheel  and  make  sure  that  it  is  not  such 
as  shall  cause  resonance. 

Wave  Form. — It  is  often  specified  that  the  e.m.f.  when  plotted 
on  a  polar  diagram,  shall  not  deviate  radially  more  than  5  per 
cent,  from  a  circle;  it  must  be  remembered,  however,  that -the 
serious  trouble,  due  to  a  bad  wave  form,  is  generally  due  to  the 
higher  harmonics  and  these  harmonics  are  usually  well  within  the 
5  per  cent,  specified. 

Temperature  Rise. — In  turbo  generators  the  temperature  rise 
by  thermometer  is  misleading,  particularly  in  the  case  of  the 
rotor,  and  specifications  for  these  machines  should  call  for 
the  temperature  rise  to  be  determined  by  the  increase  in  elec- 
trical resistance;  a  convenient  figure  to  remember  is  that  10  per 
cent,  increase  in  the  resistance  of  copper  is  equivalent  approx- 
imately to  25  per  cent,  increase  in  temperature. 

In  high  voltage  machines  the  stator  temperature  should 
be  determined  from  resistance  measurements,  and  in  the 
case  of  large  and  important  machines  it  is  sometimes  specified 
that  the  internal  temperature  of  the  machine  at  the  hottest 
part  shall  be  measured  by  a  thermo-couple  built  into  a  coil 
or  by  the  increase  in  resistance  of  a  number  of  turns  of  fine 
wire  wound  round  a  coil  before  it  is  insulated;  this  coil  is  placed 
as  near  the  neutral  of  the  machine  as  possible. 

227.  Effect  of  Voltage  on  the  Efficiency. — Consider  the  case  of 
two  machines  built  on  the  same  frame  and  for  the  same  output 
and  speed  but  for  different  voltages. 


316  ELECTRICAL  MACHINE  DESIGN 

The  windage  and  friction  loss  is  independent  of  the  voltage 
since  it  depends  on  the  speed,  which  is  constant. 

The  excitation  loss  and  the  iron  loss  are  independent  of  the 
voltage,  the  winding  being  made  so  that  the  flux  per  pole  is  the 
same  for  all  voltages. 

In  order  to  have  the  same  flux  per  pole  the  total  number  of 
conductors  must  be  directly  proportional  to  the  voltage,  and  if 
the  total  amount  of  copper  in  the  machine  is  kept  constant  the 
size  of  the  conductor  will  be  inversely  proportional  to  the  voltage 
and  therefore  directly  proportional  to  the  current,  so  that  the 
current  density  in  the  conductors,  and  therefore  the  copper  loss, 
is  independent  of  the  voltage.  If,  however,  as  is  generally 
the  case,  the  total  amount  of  armature  copper  decreases  as  the 
voltage  increases,  on  account  of  the  space  taken  up  by  insulation, 
then  in  order  to  keep  the  copper  loss  constant  the  current  rating 
must  decrease  more  rapidly  than  the  voltage  increases  and  the 
output  become  less  the  higher  the  voltage. 

If  then  the  total  section  of  copper  is  constant  at  all  voltages, 
the  losses,  output  and  efficiency  will  be  independent  of  the 
voltage;  but  if  the  total  section  of  copper  decreases  as  the 
voltage  increases  then,  while  the  losses  remain  constant,  the 
output  and  the  efficiency  decrease  with  increase  of  voltage. 

228.  Effect  of  Speed  on  the  Efficiency. — Consider  two  machines 
built  for  the  same  kw.  output,  one  of  which  runs  at  twice  the 
speed  of  the  other,  and  assume  that 

kw. 
y 7T~2T~  =  a  constant 

also  that  j-r-  ^—r- =  a  constant 

frame  length 

both  of  which  are  approximately  true  for  machines  which  have 
more  than  10  poles,  then  the  relative  dimensions  of  the  two 
machines  are  given  in  the  following  table: 

Machine  A       Machine  B 

Output kw.  kw. 

Speed r.p.m.  2(r.p.m.) 

Poles p  1/2  (p) 

Internal  diameter  of  armature Da  y-^ 

Frame  length Lc  1.25(LC) 

Pole-pitch T  1.25  (T) 

Core  depth da  1.25  da 


SPECIFICATIONS  317 

Core  Loss.- — The  core  weight  is  approx.  =  a  const.  XDaxLcXda 
and  is  the  same  for  each  machine,  so  that  for  the  same  flux 
density  in  the  core  the  core  loss  is  independent  of  the  speed. 

^  nZIc2  Lh  H- 

Copper  loss  =  — n —        — =-   where  !!/&=  (Lc  +  1.5r)  approx. 

cir.  mil  per  cond. 

_amp.  cond.  per  inch 

—     •  «i  X  7T  D d    (jLjc~i~l.OT) 

cir.  mils  per  ampere 

„,        ,.    amp.  cond.  per.  inch  .,..,-,,,,. 
The  ratio  -T-*  — ~ —  -  is  limited  by  heating  as  shown  in 

cir.  mils  per  ampere 

Fig.  181,  page  253,  and  since  the  peripheral  velocity  is  only  25 
per  cent,  higher  in  machine  B  than  in  machine  A,  it  may  be 
assumed  that  this  ratio  has  approximately  the  same  value  in 
the  two  machines  and  the  copper  loss  is  therefore 
a  const.  XDa(Lc  +  1.5r)  in  machine  A 

Da 

and  a  const.  X^-«  (1.25Lc  +  1.9r)  in  machine  B 
l.o 

=  a  const.  XDo(0.80Lc  +  1.2T) 

so  that  the  higher  the  speed  for  a  given  output  the  lower  is  the 
copper  loss. 

Windage  Loss  is  approximately  proportional  to  the  surface  of 
the  rotor  multiplied  by  the  (peripheral  velocity)3.  The  peri- 
pheral velocity  of  machine  B  is  25  per  cent,  greater  than  that 
of  machine  A,  and  the  windage  loss  is  greater  for  the  high-speed 
than  for  the  low-speed  machine. 

Bearing  Friction  Loss.  =  a  constant XdXlX(Vb)%,  formula  13, 
page  97.  Since  the  torque  on  the  shaft  of  machine  B  is  approxi- 
mately half  that  on  machine  A,  and  the  projected  area  of  the 
bearing  =  dXl  is  directly  proportional  to  this  torque,  therefore, 
the  bearing  friction  loss 

=  a  const.  XdXlX  (Vb)%  in  machine  A 
=  a  const.  X— p— X(x/2.V&)$  in  machine  B 
-a  const.  XdXlX(Vb}%  X0.85  in  machine  B 

so  that  the  higher  the  speed,  the  lower  the  bearing  friction  loss. 

Excitation  Loss. — The  radiating  surface  of  the  field  coil  is  approx- 
imately =  2 (pole  waist  +  frame  length)  X  radial  length  of  field  coil. 
Machine  B  has  25  per  cent,  greater  pole  waist,  25  per  cent,  longer 
frame  length,  and  10  per  cent,  longer  poles  radially  than  has 
machine  A,  but  it  has  also  half  the  number  of  poles  and,  therefore, 
0.7  times  the  radiating  surface. 

The  permissible  watts  per  square  inch  in  machine  B  is  approxi- 


318 


ELECTRICAL  MACHINE  DESIGN 


mately  25  per  cent,  greater  than  in  machine  A,  therefore,  if  the 
total  permissible  watts  excitation  loss  in  machine  A  =  W 
the  permissible  excitation  loss  in  machine  B  =  IF  X  0.7  X  1.25 

=  0.88  W 

therefore  the   higher  the  speed,  the  lower  the  field  excitation 
loss. 


100 


95 


3      90 


R.P.M. 

720 
200 
1800 


1000 


2000  3000 

Eilo-volt  Amperes 


4000 


5000 


FIG.  208. — Efficiency  curves  for  2400  volt  alternators. 

It  may  therefore  be  stated  as  a  general  rule,  that  the  higher 
the  speed  of  a  machine  for  a  given  rating  in  kilowatts  the  lower 
are  the  losses  and  the  higher  the  efficiency. 

Fig.  208  shows  curves  of  efficiency  for  polyphase  alternators 
wound  for  2400  volts. 


CHAPTER  XXVIII 
ELEMENTARY  THEORY  OF   OPERATION 

229.  The  Revolving  Field.— P,  Fig.  209,  shows  the  essential 
parts  of  a  two-pole  two-phase  induction  motor.  The  stator  or 
stationary  part  carries  two  windings  M  and  JV  spaced  90  electrical 
degrees  apart.  These  windings  are  connected  to  a  two-phase 
alternator  and  the  currents  which  flow  at  any  instant  in  the  coils 
M  and  N  are  given  by  the  curves  in  diagram  Q ;  at  instant  A  for 
example,  the  current  in  phase  l=-\-Im  while  that  in  phase 
2  =  zero. 

The  windings  of  each  phase  are  marked  S  and  F  at  the  termi- 
nals and  these  letters  stand  for  start  and  finish  respectively; 
a  +  current  is  one  that  goes  in  at  S,  and  a  —  current  one  that 
goes  in  at  F. 

The  resultant  magnetic  field  produced  by  the  windings  M 
and  N  at  instants  A,  B,  C  and  D  is  shown  in  diagram  R  from 
which  it  may  be  seen  that,  although  the  windings  are  stationary, 
a  revolving  field  is  produced  which  is  of  constant  strength  and 
which  moves  through  the  distance  of  two  pole-pitches  while  the 
current  in  one  phase  passes  through  one  cycle. 

To  reverse  the  direction  of  rotation  of  this  field  it  is  necessary 
to  reverse  the  connections  of  one  phase. 

P,  Fig.  210,  shows  the  winding  for  a  two-pole  three-phase 
motor;  M,  N  and  Q,  the  windings  of  the  three  phases,  are 
spaced  120  electrical  degrees  apart.  These  windings  are  con- 
nected to  a  three-phase  alternator  and  the  currents  which  flow 
at  any  instant  in  the  coils  M,  N  and  Q  are  given  by  the  curves 
in  diagram  R. 

The  resultant  magnetic  field  that  is  produced  by  the  windings 
at  instants  A,  B,  C  and  D  is  shown  in  diagram  S  from  which  it 
may  be  seen  that,  just  as  in  the  case  of  the  two-phase  machine, 
a  revolving  field  is  produced  which  is  of  constant  strength  and 
which  moves  through  the  distance  of  two  pole-pitches  while  the 
current  in  one  phase  passes  through  one  cycle. 

To  reverse  the  direction  of  rotation  of  this  field  it  is  necessary 

319 


320 


ELECTRICAL  MACHINE  DESIGN 


to  interchange  the  connections  of  two  of  the  phases;  for  example, 
to  connect  phase  2  of  the  motor  to  phase  3  of  the  alternator  and 
phase  3  of  the  motor  to  phase  2  of  the  alternator. 


FIG.  209. — The  revolving  field   of  a  two-pole  two-phase  induction  motor. 


230.  Multipolar  Motors. — Fig.  211  shows  the  winding  for  a 
four-pole,  two-phase  motor  and  also  the  resultant  magnetic  field 
at  the  instants  A  and  B,  Fig.  209.  The  field  moves  through 
the  distance  of  1/2 (pole-pitch)  while  the  current  in  one  phase 
passes  through  1/4 (cycle). 


ELEMENTARY  THEORY  OF  OPERATION       321 

Fig.  212  shows  the  winding  for  a  four-pole,  three-phase  motor 
and  also  the  resultant  magnetic  field  at  the  instants  A  and  B, 
Fig.  210.  In  this  case  the  field  moves  through  the  distance  of 


A  B  C  D 


A 

Ii-  Im 

h=-y2im 

Is=-l/2lm  73=-/w          & 

FIG.  210. — The  revolving  field  of  a  two-pole  three-phase  induction  motor. 

1/3 (pole-pitch)  while  the  current  in  one  phase  passes  through 
l/6(cycle). 

In  general  the  field  moves  through  the  distance  of  two  pole- 
21 


322 


ELECTRICAL  MACHINE  DESIGN 


pitches  or  through  -  of  a  revolution  while  the   current  in  one 
phase  passes  through   one   cycle,   therefore,   the  speed  of  the 


revolving  field   ==-  X/  revolutions  per  second 


120X/ 
P 


revolutions  per  minute 


(42) 


this  is  called  the  synchronous  speed. 


Diagrammatic  Representation  of  a  4  Pole  2  Phase 
Induction  Motor 


FIG.  211. — The  revolving  field  of  a  four-pole  two-phase  induction  motor. 

231.  Induction  Motor  Windings. — The  conditions  to  be  fulfilled 
by  these  windings  are  that  the  phases  should  be  wound  alike, 
should  have  the  same  number  of  turns,  and  should  be  spaced  90 
electrical  degrees  apart  in  the  case  of  a  two-phase  winding  and 
120  electrical  degrees  apart  in  the  case  of  a  three-phase  winding. 

The  above  are  the  conditions  that  have  to  be  fulfilled  by 
alternator  windings  so  that  the  diagrams  developed  in  Chapter 
XVII  apply  to  induction  motors  as  well  as  to  alternators. 


ELEMENTARY  THEORY  OF  OPERATION        323 


Fig.  213  shows  an  actual  stator  with  its  windings  arranged  in 
phase  belts.  The  ends  of  the  coils  are  bent  back  so  that  the 
rotating  part  of  the  machine,  called  the  rotor,  can  readily  be 
put  in  position. 

The  type  of  rotor  which  is  in  most  general  use  is  shown  in 
Fig.  214  and  is  called  the  squirrel-cage  type.  It  consists  of  an 
iron  core  slotted  to  carry  the  copper  rotor  bars;  these  bars  are 


Diagrammatic  Representation  of  a  4  Pole  3  Phase 
Induction  Motor 


FIG.  212. — The  revolving  field  of  a  four-pole  three-phase  induction  motor. 

joined  together  at  the  ends  by  brass  end  connectors  so  as  to  form 
a  closed  winding. 

232.  Rotor  Voltage  and  Current  at  Standstill. — The  actions  and 
reactions  of  the  stator  and  rotor  will  be  taken  up  later;  it  is  neces- 
sary, however,  to  point  out  here  that,  since  the  applied  voltage 
per  phase  is  constant,  the  back  voltage  per  phase  must  be  approxi- 
mately constant  at  all  loads.  This  back  voltage  is  produced  by 
the  revolving  field,  therefore,  the  actions  and  reactions  of  the 


324 


ELECTRICAL  MACHINE  DESIGN 


stator  and  rotor  must  be  such  as  to  keep  the  revolving  field 
approximately  constant  at  all  loads. 

Let  the  revolving  field  be  represented  by  a  revolving  north 
and  south  pole  as  shown  in  diagram  A,  Fig.  215,  and  then  for 
convenience  let  this  figure  be  split  at  xy  and  opened  out  on  to  a 
plane;  the  result  will  be  diagram  B,  of  which  a  plan  is  shown  in 
diagram  D. 


FIG.  213. — Stator  of  an  induction  motor. 


The  distribution  of  flux  on  the  rotor  surface  due  to  the  revolv- 
ing field  is  given  by  the  curve  in  diagram  B  at  a  certain  instant. 
The  field  is  moving  in  the  direction  of  the  arrow;  it  therefore  cuts 
the  rotor  bars  and  generates  in  them,  e.m.fs.  which  are  shown  in 
magnitude  at  the  same  instant  in  diagram  D.  Since  the  rotor 


ELEMENTARY  THEORY  OF  OPERATION        325 


circuit  is  closed  these  e.m.fs.  will  cause  currents  to  flow  in  the 
rotor  bars. 

The  frequency  of  the  e.m.fs.  in  the  rotor  bars  at  standstill 

—     '          -  cycles  per  second  =  the  frequency  of  the  stator 

applied  e.m.f.,  so  that  the  frequency  of  the  rotor  currents  is  high, 
and  the  reactance  of  the  rotor,  which  is  proportional  to  this  fre- 
quency, is  large  compared  with  its  resistance;  the  rotor  current 


FIG.  214. — Squirrel  cage  rotor. 

therefore  lags  considerably  behind  the  rotor  voltage  as  shown 
by  the  curve  in  diagram  D  and  also  by  crosses  and  dots  in  dia- 
gram C.     The  value  of  this  current  at  standstill 
_  rotor  voltage  at  standstill 

rotor  impedance  at  standstill 
and  this  is  usually  about  5.5  times  the  full-load  rotor  current. 

233.  Starting  Torque. — As  shown  in  diagrams  C  and  D  the 
rotor  bars  are  carrying  current  and  are  in  a  magnetic  field  so  that 
a  force  is  exerted  tending  to  move  them ;  this  force  when  multiplied 
by  the  radius  of  the  rotor  gives  the  torque.  The  relative  torque 
at  different  points  on  the  rotor  surface  is  given  by  the  curve  in 
diagram  D,  which  is  got  by  multiplying  the  value  of  flux  density 


326 


ELECTRICAL  MACHINE  DESIGN 


at  different  points  on  the  rotpr  surface  by  the  value  of  the  current 
in  the  rotor  bar  at  these,  points.  It  may  be  seen  from  this  curve, 
and  also  from  diagram  C,  that  at  some  points  on  the  rotor  sur- 
face the  torque  is  in  one  direction  and  at  other  points  is  in  the 
opposite  direction  so  that  the  resultant  torque  is  quite  small. 

N 


ooooooooooooo 


\\1 


---  Torque 


Rotor  Voltage 


Rotor  Current 


FIG.  215. — Production  of  torque  in  an  induction  motor. 

As  a  rule  the  starting  torque  of  a  squirrel-cage  motor  is  about  1.5 
times  full-load  torque  when  the  rotor  current  is  about  5.5  times 
the  full-load  rotor  current.  Diagram  C  shows  that  the  resultant 
torque  is  in  such  a  direction  as  to  tend  to  make  the  rotor  follow 
up  the  revolving  field. 


ELEMENTARY  THEORY  OF  OPERATION        327 

The  starting  torque  can  be  increased  for  a  given  current  if  that 
current  be  brought  more  in  phase  with  the  voltage,  this  can  read- 
ily be  seen  from  the  curves  in  Fig.  215.  The  angle  of  lag  of  the 
rotor  current  can  be  decreased  by  increasing  the  rotor  resistance, 
and  sufficient  resistance  is  generally  put  in  the  rotor  circuit  to 
bring  the  current  down  to  its  full-load  value;  the  angle  of  lag  is 
thSn  so  small  that  full-load  torque  is  developed. 

When  a  motor  is  running  under  load  a  large  rotor  resistance 
is  undesirable  because  it  causes  large  loss,  low  efficiency,  and 


1"'  15  1U>. 


TV  ft-;  •  K"  KOTOH. 


FIG.  216. — Wound  rotor  type  of  induction  motor. 

excessive  heating.  To  get  over  this  difficulty  the  wound  rotor 
motor  was  developed.  This  type  of  motor  has  the  same  stator 
as  that  used  for  the  squirrel-cage  machine  but  its  rotor  is  as 
shown  in  Fig.  216;  the  rotor  bars  are  connected  together  to  form 
a  winding,  but  this  winding  is  not  closed  on  itself  as  in  the  squirrel- 
cage  machine,  it  is  left  open  at  three  points  which  are  connected 
to  three  slip  rings,  and  the  winding  is  closed  outside  of  the  ma- 
chine through  resistances  which  can  be  adjusted.  The  winding 
is  finally  short  circuited  at  the  slip  rings  when  the  motor  is  up 


328 


ELECTRICAL  MACHINE  DESIGN 


to  speed.  In  this  way  it  is  possible  to  have  the  advantage  of 
high  rotor  resistance  for  starting  and  low  rotor  resistance  when 
the  motor  is  running  at  full  speed. 

234.  Running  Conditions. — It  was  pointed  out  in  the  last  arti- 
cle that  the  resultant  torque  is  in  such  a  direction  as  to  make 
the  rotor  follow  up  the  revolving  field.  When  the  motor  is  not 
carrying  any  load  the  rotor  will  revolve  at  practically  synchro- 
nous speed,  that  is,  at  the  speed  of  the  revolving  field.  If  the 
motor  is  then  loaded  it  will  slow  down  and  slip  through  the  revolv- 
ing field,  the  rotor  bars  will  cut  lines  of  force,  the  e.m.fs.  generated 
in  these  bars  will  cause  currents  to  flow  in  them  and  a  torque  will 
be  produced.  The  rotor  will  slow  up  until  the  point  is  reached 
at  which  the  torque  developed  by  the  rotor  is  equal  to  the  torque 
exerted  by  the  load. 

rp,          ,.    syn.  r.p.m.  —  r. p.m.  of  rotor  . 

The  ratio  -  -  is  called  the  per   cent, 

syn.  r.p.m. 

slip  and  is  represented  by  the  symbol  s,  its  value  at  full-load  is 
generally  about  4  per  cent. 


400 


800   1000   1200   1400 
R.P.M. 


FIG.  217. — Characteristics  of  a  25-h.p.,  440-volt,  3-phase,  60-cycle,  1200  syn. 
r.p.m.  induction  motor. 

As  the  load  is  increased  the  rotor  drops  in  speed  and  the  slip, 
rotor  current,  frequency  and  lag  of  rotor  current  all  increase. 
The  torque  developed  by  the  rotor  tends  to  increase  due  to  the 
increase  in  rotor  current  and  to  decrease  due  to  the  increase  in 
current  lag.  Up  to  a  certain  point,  called  the  break-down  point 
or  point  of  maximum  torque,  the  effect  of  the  current  is  greater 


ELEMENTARY  THEORY  OF  OPERATION        329 

than  that  of  the  current  lag,  beyond  that  point  the  effect  of  the 
current  lag  is  the  greater,  so  that  after  the  break-down  point  is 
passed  the  torque  actually  decreases  even  although  the  current 
is  increasing. 

The  relation  between  speed,  torque,  and  current  is  shown  in 
Fig.  217  fora  25-h.  p.,  440-volt,  three-phase,  60-cycle,  1200-syn. 
r.p.m.  induction  motor. 

235.  Vector  Diagram  at  No-load. — At  no-load  a  motor  runs  at 
synchronous  speed  so  that  the  slip,  rotor  voltage  and  rotor  cur- 
rent are  all  zero. 

Consider  the  winding  S1F1  of  one  phase  of  the  stator  as  shown 
in  Fig.  209  or  210.  The  voltage  El  applied  to  this  phase  causes 
a  current  70,  called  the  magnetizing  current,  to  flow  in  the  winding. 
This  current,  along  with  the  magnetizing  currents  in  the  other 
phases,  produces  a  revolving  field  <£/  of  constant  strength. 

While  the  revolving  field  (/>/  is  of  constant  strength  the  flux 
(/)g  which  threads  the  winding  SlFl  is  an  alternating  flux  and 
is  a  maximum  and  =  (/>/  when  the  magnetizing  current  in  the 
winding  SLFl  is  a  maximum;  this  can  be  ascertained. by  exami- 
nation of  diagram  R,  Fig.  209  and  of  diagram  S,  Fig.  210,  so  that 
the  flux  which  threads  the  winding  $,1^  is  in  phase  with  the 
magnetizing  current  70  in  that  winding. 

The  alternating  flux  <j)g  generates  an  alternating  e.m.f.  Erf 
called  the  back  e.m.f.  in  the  winding  S^^,  and  this  voltage  lags 
the  flux  <J)g  by  90°.  To  overcome  this  back  e.m.f.  the  applied 
e.m.f.  must  have  a  component  which  is  equal  and  opposite  to 
Erf  at  every  instant;  the  other  component  of  the  applied  e.m.f. 
must  be  large  enough  to  send  a  current  70  through  the  impedance 
of  the  winding. 

In  Fig.  218 

I0      is  the  magnetizing  current  in  one  phase, 
<pg    is  the  flux  per  pole  threading  that  phase, 
Erf   is  the  back  e.m.f.  in  that  phase  of  the  stator  and  lags  (f)g 

which  produces  it  by  90°, 
En    is  the  component  of  the  applied  e.m.f.  which  is  equal  and 

opposite  to  Erf, 
/0Z1  is  the  component  of  the  applied  e.m.f.  which  is  required  to 

send  the  current  70  through  the  stator  impedance  Zt, 
EI     is  the  applied  voltage  per  phase  and  is  the  resultant  of  E1 l 

and  IQZr 

236.  Vector  Diagram  at  Full -load.— At  full-load  the  speed  of 


330 


ELECTRICAL  MACHINE  DESIGN 


the  rotor  =  r.p.m.2  =  (1  — s)r.p.m.1,  and  the  speed  of  the  revolving 
field  relative  to  the  rotor  surf  ace  =  s(r.p.m.1);  so  that  the  frequency 
of  the  e.m.f.  which  is  generated  in  the  rotor  winding  by  the 

i   •      ^  u      sfr.p.m.jXp       - 
revolving  field  =—  ^TT,A          =sfi- 
\-Zi\j 

The  flux  (j)g  threads  the  rotor  coils  and  generates  in  each  phase 
of  the  rotor  winding  a  voltage  E2  which  lags  <f>g  by  90°.     This 

T7I 

voltage  causes  a  current  72  =  ~-  to  flow  in  the  closed  rotor  circuit; 

^2 

sX 

72  lags  the  voltage  E2  by  an  angle  whose  tangent  =  -=-*, 

H2 

where  Z2  is  the  rotor  impedance  at  full-load, 

X2  is  the  rotor  reactance  per  phase  at  standstill, 

R2  is  the  rotor  resistance  per  phase, 

s,  the  per  cent,  slip,  is  approximately  =  4  per  cent., 


E 


El 


FIG.  218.  —  No-load  vector  diagram. 


FIG.  219.  —  Vector  diagram 
at  full  load. 


with  this  value  of  s  the  angle  of  lag  of  the  rotor  current  at  full 
load  seldom  exceeds  20°. 

In  Fig.  219 
/0     is  the  magnetizing  current,  which  has  the  same  value  as  in 

Fig.  218, 

<j>g   is  the  flux  per  pole  threading  one  phase  of  both  rotor  and 
stator  windings, 


ELEMENTARY  THEORY  OF  OPERATION        331 

E^b  is  the  back  e.m.f.  of  the  stator, 

E2    is  the  e.m.f.  generated  in  one  phase  of  the  rotor  by  flux  <j>g, 

72     is  the  current  in  that  phase, 

E^    is  the  component  of  the  applied  e.m.f.  which  is  equal  and 

opposite  to  EL&., 

Now  Elf  the  applied  voltage,  is  constant  and  is  the  resultant 
of  7?u  and  7^;  this  latter  quantity  is  comparatively  small  even 
at  full-load,  so  that  it  may  be  assumed  that  En  has  the  same 
value  at  full-load  as  at  no-load  and  therefore  E^,  which  is  equal 
and  opposite  to  Ell  and  (j)g  which  produces  E^,  are  approxi- 
mately constant  at  all  loads,  so  that  the  resultant  magnetiz- 
ing effect  of  the  stator  and  rotor  currents  must  be  equal  to  the 
magnetizing  effect  of  the  current  I0.  The  stator  current  may 
therefore  be  divided  into  two  components,  one  of  which  7U  has 
a  m.m.f.  equal  and  opposite  to  that  of  the  rotor  current  72;  the 
other  component  of  stator  current  must  be  I0,  because  this  is  the 
necessary  condition  for  a  constant  value  of  $g  and  of  E^', 
therefore,  in  Fig.  219,  7U  is  a  component  of  primary  current  whose 
m.m.f.  is  equal  and  opposite  to  that  of  72. 
7,  is  the  primary  current  and  is  the  resultant  of  I0  and  7U. 
E{  is  the  applied  voltage  and  is  the  resultant  of  El}  and  7tZr 


CHAPTER  XXIX 

GRAPHICAL  TREATMENT  OF  THE  INDUCTION 
MOTOR 

237.  Current  Relations  in  Rotor  and  Stator. — It  is  shown  in 
Art.  236  that  the  m.m.f.  of  the  rotor  opposes  that  of  the  stator, 
and  that  the  resultant  m.m.f.,  namely,  that  of  the  magnetiz- 
ing current,  is  just  sufficient  to  produce  the  constant  revolving 
field  <f>f. 

Fig.  220  shows  the  position  of  the  windings  of  one  phase  of  both 
rotor  and  stator,  and  also  the  direction  of  the  currents  in  these 


Staler 


Rotor 


FIG.  220. — The  magnetic  fields  in  an  induction  motor. 


windings,  at  the  instant  that  the  rotor  and  stator  m.m.f s.  are 
directly  opposing  one  another.  As  the  rotor  revolves  relative 
to  the  stator  there  will  be  positions  on  either  side  of  that  shown 
in  Fig.  220,  in  which  the  rotor  and  stator  m.m.fs.  do  not  quite 
oppose  one  another;  two  such  positions  are  shown  in  Fig.  221; 
this  overlapping  of  the  phases  is  called  the  belt  effect  and  is  dis- 
cussed more  fully  in  Chap.  33. 

Due  to  the  revolving  field  (j>f  an  alternating  flux  <j>g  threads 
one  phase  of  both  rotor  and  stator  windings.  It  is  shown  in  Fig. 
220  that,  in  addition  to  the  flux  $g  which  crosses  the  air-gap, 
there  is  a  leakage  flux  (f>ti  which  links  the  stator  coils  but  does  not 
cross  the  air-gap;  0^  is  proportional  to  the  current  It  which 
produces  it.  There  is  also  a  leakage  flux  (f>2i  which  links  the  rotor 

332 


GRAPHICAL  TREATMENT 


333 


coils  but  does  not  cross  the  air-gap;  <j>2i  is  proportional  to  the 
current  72  which  produces  it. 

238.  The  Stator  and  Rotor  Revolving  Fields.— 
If  /!      =the  frequency  of  the  stator  current, 

s       =the  per  cent,  slip, 
r.p.m.1=the  synchronous  speed, 


X 


FIG.  221. — Overlapping  of  the  phases. 

then/2,  the  frequency  of  the  rotor  current  =  s/1?  see  Art.  236, 
and  (1  — s)r.p.m.1=  the  rotor  speed. 

The  stator  current  acting  alone  produces  a  field  which  revolves 
at  synchronous  speed,  namely  r.p.m.j;  the  rotor  current  acting 
alone  produces  a  field  which  revolves  at  a  speed  of  s(r.p.m.1) 
relative  to  the  rotor  surface  or  at  sCr.p.m.J  +  (1  -s)r.p.m.1  =  r.p.m.! 
relative  to  the  stator  surface;  that  is,  the  two  fields  revolve  at 
the  same  speed  in  space  and  so  can  be  represented  on  the  same 
diagram. 

239.  The  Voltage  and  Current  Diagram. — Fig.  224  shows  the 
voltage  and  current  relations  in  an  induction  motor. 

EI  =the  voltage  per  phase  applied  to  the  stator  windings, 
/!=the  stator  current  per  phase,  and  lags  E^  by  6  degrees;  the 
locus  of  /!  is  a  circle. 

240.  The  Flux  Diagram. — Consider  the  stator  current  acting 
alone,  then  in  Fig.  222: 


334  ELECTRICAL  MACHINE  DESIGN 

<j)l    =the  flux  per  pole  threading  one  phase  of  the  stator  and,  as 

pointed  out  in  Art.  2357  page  329,  is  in  phase  with  7t, 
<j)vi  =the  stator  leakage  flux  per  phase  per  pole,  see  Fig.  220, 
<£j0  =  that  part  of  (f>i  which  crosses  the  gap  and  threads  one 

phase  of  the  rotor  =  v^. 

Consider  the  rotor  current  72  acting  alone,  then: 
02    =the  flux  per  pole  threading  one  phase  of  the  rotor, 
cp2i   =the  rotor  leakage  flux  per  phase  per  pole, 
(j)2g  =that  part  of  </>2  which  crosses  the  garj  and  threads  one 

phase  of  the  stator  =  v2^f)2. 

Under  load  conditions,  when  both  1^  and  72  are  acting, 
</>ls  =the  actual  flux  per  pole  threading  one  phase  of  the  stator, 
(j)2r  =the  actual  flux  per  pole  threading  one  phase  of  the  rotor, 
<j)g    =the  actual  flux  per  pole  in  the  gap  between  rotor  and  stator, 
Elb  =the  stator  e.m.f.  per  phase  generated  by  <j)ia  and  consists 
of  two  components; 
Eig  generated  by  the  flux  (f>g 
E^i  =I^X1}  generated  by  the  flux^z 

E2g  =  the. rotor  e.m.f.  per  phase  generated  by  </>g.  This  e.m.f. 
sends  a  current  72  through  the  rotor  winding  which  pro- 
duces the  leakage  flux  <j>2i  and  generates  the  e.m.f. 
E2i  =  I2X2  in  that  winding. 

E2g,  therefore,  consists  of  two  components,  namely, 
E2r  to  overcome  the  resistance  per  phase  and  a  voltage 
equal  and  opposite  to  E2i  to  overcome  the  reactance  per 
pha&e. 

Since  E2r  is  in  phase  with  72  and  therefore  with  </>2,  the  angle 
aoh  =  angle  oab  =  90°. 

The  applied  voltage  must  be  equal  and  opposite  to  E^  if  the 
stator  resistance  per  phase  and  therefore  the  voltage  IlRl  is 
sufficiently  small  to  be  neglected.  Since  El  is  constant,  therefore 
E^b,  and  the  flux  <j>is  which  produces  E^,  must  be  constant  in 
magnitude. 

241.  Geometrical  Proof  of  the  Circle  Law.— In  Fig.  222  draw 
dk  perpendicular  to  fd  so  as  to  cut  the  line  of  produced  at  k. 
In  triangles  aob  and  fdk, 

angle  oab  ;=  angle  fdk  =  90°, 
angle  oba=  angle  dfkt 

fk     fd         fd  fd 

therefore,  f  =  —7  =  —    — j-  =  ~^r r 

ob      ab     ac  —  cb     oh—cb 


GRAPHICAL  TREATMENT 


335 


and 


oh-cb 

(v1Xof)(v2Xoh) 
oh(l  —  v^Vz) 


=  a  constant,  since  v1}  v2,  and  of  are  all 
constant. 

Since  fk  is  constant  and  angle  fdk  is  an  angle  of  90°,  the  locus 
of  d,  or  of  0j,  is  a  circle  whose  center  is  on  the  line  ok  and  whose 
diameter  =fk. 

If  the  magnetic  circuit  be  not  saturated,  and  this  is  the  case 
at  the  actual  flux  densities  due  to  <j>18  and  <f>2r,  the  actual  fluxes 
in  the  machine,  then  Fig.  222  may  be  transformed  into  Fig.  223, 


FIG.  222.  —  Voltage  and  flux  diagram. 


pro- 


which  is   a  m.m.f.  and  voltage  diagram,  by  making  njb 
portional  to  <^  and  njb2cJ2  proportional  to  </>2. 

Fig.  223  may  be  transformed  into  a  voltage  and  current  dia- 
gram as  shown  in  Fig.  224,  and  in  this  form,  with  a  slight  modi- 
fication, it  is  generally  used. 

242.  Special  Cases.  —  1.  The  motor  is  running  without  load 
and,  therefore,  at  synchronous  speed,  so  that  the  rotor  e.m.f. 
and  the  rotor  current  are  zero.  Under  these  conditions  Fig.  224 
becomes  Fig.  225. 


336 


ELECTRICAL  MACHINE  DESIGN 


2.  The  motor  is  at  standstill  and  the  rotor  resistance  is  assumed 
to  be  zero.  Under  these  conditions  Figs.  222  and  224  give  Fig. 
227.  Since  R2  is  zero  therefore  E2r  and  </>2r  are  both  zero,  and 
E2g  must  be  equal  and  opposite  to  E2i  and  therefore  equal  to  I2X2. 

Now  Elb=Eig+Eli 


FIG.  223. — Voltage  and  m.m.f.  diagram. 

HE> 


FIG.  224.  —  Voltage  and  current  diagram 
and  —^——^  since  they  are  produced  by  the  same  flux 


E 


2g 


therefore  E^ 


22 


Y 
^ 


GRAPHICAL  TREATMENT 


337 


(43) 


the  value  of  It  in  this  case  is  Id  the  maximum  current,  Fig.  224. 
243.  Representation  of  the  Losses  on  the  Circle  Diagram. — 

The  losses  in  an  induction  motor  are: 

Mechanical  losses — windage  and  friction  loss. 
Constant  losses    Iron  or  core  loss — hysteresis  and  eddy -current 

loss. 

f  Stator  copper  loss. 
Variable  losses  |  Rotor  copper  loss. 
[  Load  losses. 


No-load  conditions. 

Constant  Losses. — As  a  motor  is  loaded,  the  rotor  drops  in 
speed  and  the  slip  and  therefore  the  frequency  of  the  flux  in  the 
rotor  core  increases.  Due  to  the  drop  in  speed  the  windage  and 
friction  loss  decrease  and  due  to  the  increase  in  frequency  of  the 
rotor  flux 'the  iron  loss  in  the  rotor  core  increase?,  so  that  it  is 
reasonable  to  assume  that  the  sum  of  these  two  losses  is  constant 
at  all  speeds. 

To  overcome  the  constant  loss  a  stator  current  Iwo  is  required, 
in  phase  with  the  applied  voltage  and  of  such  a  value  that  n^EJwo 
=  the  constant  loss  in  watts.  To  take  account  of  this  in  the 
circle  diagram  the  no-load  conditions  have  to  be  changed  from 
those  of  Fig.  225  to  those  of  Fig.  226. 

Variable  Losses. — These  are  nJ2Jt^  and  n2I22R2. 

In  Fig.  224  the  stator  current  =  7t  and  the  corresponding  rotor 


current  =  /2=/11X— X 


1  *  1 


n2b2c2 


338  ELECTRICAL  MACHINE  DESIGN 

The  Rotor  Copper  Loss.— This  loss  =  n2I22R2  watts 


T — 

n2b2c2 


=  /2uXa  constant. 
\  Fig.  224 


Now 


=  xD;  where  D  is  a  constant 
therefore  the  rotor  loss  =  x(a  constant). 

To  allow  for  the  rotor  loss  on  the  circle  diagram  take  any 
stator  current  Ilt  find  the  corresponding  rotor  current  72  and 
the  rotor  copper  loss  n2P2R2  in  watts;  set  up  from  the  base  line 


c      k 


E2 


FIG.  227. — Conditions  at  standstill  with  zero  rotor  and  stator  resistance. 

old  a  current  Irw  as  shown  in  Fig.  224,  in  phase  with  Elt  such 
that  niElIrw  =  the  rotor  copper  loss  in  watts.  Draw  a  straight 
line  through  I0  and  Irw.  The  vertical  distance  from  the  base  to 
this  line  is  proportional  to  x  and  is  a  measure  of  the  rotor  loss. 

The  Stator  Copper  Loss.— This  Ioss  =  n1/21#1  watts.  I\  is 
assumed  to  be  =  /20+/2u;  the  error  due  to  this  assumption  is 
comparatively  small.  The  part  of  the  copper  loss  nlP0Rl  is 
added  to  the  constant  losses,  the  other  part  nlPllRL  is  propor- 
tional to  x  just  as  in  the  case  of  the  *otor  loss. 

To  allow  for  the  stator  loss  on  the  circle  diagram  take  any 
stator  current  /l;  find  the  corresponding  stator  copper  loss  n^P^R^ 
in  watts;  set  up  from  the  line/w,  Fig.  224,  a  current  I8W  in  phase 
with  E17  such  that  n1£'1/sw  =  the  stator  copper  loss  in  watts. 
Draw  a  straight  line  through  I0  and  Isw. 


GRAPHICAL   TREATMENT 


339 


Load  Losses. — These  consist  of  various  eddy-current  losses 
which  cannot  be  accurately  predetermined  and  which  are*  made 
as  small  as  possible  by  careful  design;  they  are  usually  allowed  for 
by  increasing  the  variable  losses  by  a  certain  percentage  found 
from  tests  on  similar  machines. 

244.  Relation  Between  Rotor  Loss  and  Slip. — Let  the  curve  in 
Fig.  228  represent  the  distribution  of  the  actual  rotor  revolving 
field  (j)r  corresponding  to  the  alternating  flux  02r,  Fig.  222. 


FIG.  228.  —  Torque  on  a  rotor  conductor. 

The  e.m.f.  generated  in  a  rotor  conductor  by  this  flux 
-2.22  0r2  10-8  volts 


-2.22     5rwrLc     (s/J  10  ~8  volts 

and  is  in  phase  with  the  flux  density. 

It  is  shown  in  Fig.  222  that  72  is  in  phase  with  the  voltage  E2r 
so  that  the  loss  per  conductor 

=  E2rXl2  watts 

-2.22  Br  m2TLcs/;/210-8  watts. 

71 

Since  72  is  in  phase  with  E2r  it  is  also  in  phase  with  the  flux 
density  so  that  the  average  force  on  a  rotor  conductor 


=  Br  eff 


c  dynes,  where  Br  and  Lc  are  in 


centimeter  units 
and  the  work  done  by  this  conductor  in  ergs  is  therefore 

=  Br  effX  j^Xl/cXcond.  velocity  in  centimeters  per  second 


340 


ELECTRICAL  MACHINE  DESIGN 


Br  m  7 


=  —T=-  |Y)  XLcXn  (rotor  diameter  X  revolutions  per  second) 


or  in  watts 


rotor  loss 
therefore,  - 


rotor  output     1  —  s 

,    rotor  input         1 
and  -  ~T  =  ^ — 

rotor  output     1  —  s 

_  synchronous  speed 

actual  speed 

245.  The  Final  Form  of  the  Circle  Diagram.— Fig.  229  shows 
the  form  in  which  the  circle  diagram  is  generally  used. 


FIG.  229. — The  circle  diagram. 

For  a  stator  current  71=oc  =  full-load  current 

gc   =the  power  component  of  the  primary  current 

fg    =that  part  of  gc  required  to  overcome  the  constant  losses 

ef   =that  part  of  gc  required  to  overcome  the  stator  copper  loss 

de  =that  part  of  gc  required  to  overcome  the  rotor  copper  loss 

cd  =that  part  of  gc  required  to  overcome  the  mechanical  load 


-  =the  power  factor 


eg 
oc 
cd 

eg 

dc 
ce 
de 
ce 


the  efficiency 

rotor  output 
rotor  input 
rotor  loss 


actual  speed 
synchronous  speed 


rotor  input 


=  s  =  per  cent,  slip 


the  h.  p.  output  =• 


746 


GRAPHICAL   TREATMENT  341 


,.  _,       ^.      33000 

the  corresponding  torque,  ^  —  "^74^  —  X~  --  lb.  at   1   ft. 

radius. 

At  synchronous  speed  this  same  torque  would  produce 

.i  , 

-  horse-power 

.  .  .,  . 

=     74.fi"     norse-Power;'     this     is     called    the 

Synchronous  Horse-power  due  to  full-load  torque. 

At  standstill  the  synchronous  horse-power  due  to  the  starting 

n+E.(lm)     the  rotor  copper  loss  in  watts 
torque  =  -  JS_ 


The  maximum  horse-power  output  of  the  motor 
_nlEl  (maximum  value  of  dc) 

746 
The  maximum  torque  is  that  which  gives  a  synchronous  horse- 

n.E*  (maximum  value  of  ce\ 
power  =  -JW- 

The  use  of  this  circle  diagram  is  shown  by  an  example  which  is 
worked  out  fully  in  the  next  chapter. 


CHAPTER  XXX 


CONSTRUCTION  OF  THE  CIRCLE  DIAGRAM  FROM   TESTS 

The  no-load  saturation  and  the  short-circuit  tests  are  those 
that  are  usually  made  on  an  induction  motor  in  order  to  de- 
termine its  characteristics. 

246.  The  No-load  Saturation  Curve. — The  figures  necessary  for 
the  construction  of  this  curve  are  got  by  running  the  motor  at 
normal  frequency  and  without  load.  Starting  at  50  per  cent, 
above  normal  voltage,  the  voltage  is  gradually  reduced  until  the 
motor  begins  to  drop  in  speed  and  simultaneous  readings  are 
taken  of  voltage,  current  and-  total  watts  input. 

The  results  of  such  a  test  on  a  50  h.  p.,  440-volt,  three-phase, 
60-cycle,  eight-pole,  Y-connected  motor  are  given  below. 

NO-LOAD  SATURATION 


I 

Et 

II 

P 

Terminal  volts 

Line  current 

Watts  input 

600 

32.3 

2,940 

562 

29.0 

2,650 

521 

25.9 

2,350 

470 

22.6 

2,100 

422 

19.8 

1,860 

375 

17.0 

1,650 

318 

14.2 

1,450 

275 

12.5 

1,300 

222 

10.5 

1,150 

175 

8.9 

1,080 

120 

7.5 

960 

In  Fig.  230:- 

The  relation  between  Et  and  //  is  shown. in  curve  1, 
The  relation  between  Et  and  P  is  shown  in  curve  2, 
The  straight  line,  curve  3,  shows  the  relation  between  Et  and 
that  part  of  the  exciting  current  which  is  required  to  send  the 
magnetic  flux  across  the  air  gap;  this  curve  is  calculated  by 

342 


CONSTRUCTION  OF  THE  CIRCLE  DIAGRAM    343 

the  method  explained  in  Chap.  XXXII.  At  normal  voltage  the 
exciting  current  is  21  amperes,  the  magnetizing  current  required  to 
send  the  magnetic  flux  across  the  air-gap  is  17.6  amperes,  and 


21 

the  ratio  -~    -^  =l.2Q  = 
17.  b 


which  is  called  the  iron  factor. 


Curve  1  is  not  tangent  to  curve  3  because,  in  addition  to  the  true 
magnetizing   current,  the   exciting  current  contains  the  power 


Terminal  Volts  =Et 

/ 

¥ 

? 

X 

/ 

g  g  i 

Values  of  /wsc 

P  r  f* 

C7<  0  CT 

/ 

/i 

9 

X 

3/ 

/ 

~" 

77 

""" 

r 

"~ 

^ 

. 

y 

/« 

X 

It 

X 

x^ 

•^ 

it 

, 

2 

x 

^ 

^ 

^ 

r^^ 

/} 

i 

I 

x 

x 

^ 

-^ 

^^ 

,  - 

"** 

/ 

/• 

^ 

^ 

^ 

^ 

G 

i 

'I 

^ 

X 

r 
^^ 

^ 

-^ 

^ 

1 

ft 

^ 

^ 

^ 

1^ 

^ 

^ 

; 

-M-  > 


0.5         1.0         1.5         2.0         2.5          3.0 

Kilowatts  at  No  Load=P0 
10          20          30          40 
Amperes  at  No  Load  =  Ie 
50         100        150        200        250        300        350 
Amperes  on  Short  Circuit  -ISc 


400 


Curve  1. 
Curve  2. 
Curve  4. 
Curve  5. 
current. 


Terminal  volts  and  exciting  current. 

Terminal  volts  and  no-load  loss. 

Terminal  volts  and  short-circuit  current. 

Short-circuit  current  and  power  component  of  short-circuit 


. 
Curve  6.—  Short-circuit  current  and 

FIG.  230 


torque  in  ft.-lbs. 


terminal  volts. 

Test  curves  on  a  50-h.p.,  440-volt,  3-ph.,  60-cycle,  900-syn. 
r.p.m.  induction  motor. 


component    Iwo    which   is  required  to  overcome  the  losses  P. 
Iwo  is  quite  large  at  low  voltages;  for  example,  at  120  volts 

Ie      =7.2  amperes 

P      =960  watts 
960 


I0  =v7.22—  4.62  =  5.6  amperes  =  the  true  magnetizing  cur- 
rent. The  difference  between  I0  and  Ie  is  comparatively  small 
at  normal  voltage,  for  example,  at  440  volts 


344 


ELECTRICAL  MACHINE  DESIGN 


Ie      =  21  amperes 

P      =1950  watts 

Iwo  =2.54  amperes 

I0      =\/212-2.542  =  20.8  amperes 

P  contains  the  windage  and  friction  loss,  the  core  loss,  and 
the  small  stator  copper  loss  due  to  the  current  Ie.  If  curve  2 
be  produced  so  as  to  cut  the  axis  as  shown,  then  the  watts  loss 
at  zero  voltage  =  800  watts,  must  be  the  windage  and  friction  loss 
since  the  flux,  and  therefore  the  core  loss,  is  zero  and  the  stator 
copper  loss  can  be  neglected. 

247.  The  Short-circuit  Curve. — This  curve  shows  the  relation 
between  stator  voltage  and  current,  the  rotor  being  at  stand- 
still. The  figures  necessary  for  its  construction  are  obtained 
by  blocking  the  rotor  so  that  it  cannot  revolve  and  applying 
voltage  to  the  stator  windings  at  normal  frequency;  the  rotor 
is  sometimes  held  by  means  of  a  prony  brake  so  that  readings 
of  starting  torque  may  also  be  taken.  The  applied  voltage  is 
gradually  raised  from  zero  to  a  value  that  will  send  about  twice 
full-load  current  through  the  motor,  and  simultaneous  readings 
are  taken  of  voltage,  current,  total  watts  input,  and  torque. 

The  results  of  such  a  test  on  the  50  h.  p.  motor  on  which  the 
saturation  test  was  made  are  given  below. 

SHORT  CIRCUIT 


E\ 

I.c 

P 

•*  wsc 

T 

T 

Et 

Terminal 
volts 

Line 
current 

Watts 
input 

Torque  in 
pounds  at  1 
ft.  radius 

222 

185 

3,000 

78 

155 

.7 

201 

165 

2,400 

69 

122 

.61 

178 

143 

1,820 

59 

94 

.53 

162 

127 

1,420 

51 

71 

.44 

138 

109 

990 

41 

51 

.37 

120 

88 

680 

33 

35 

.29 

101 

72 

440 

25 

23 

.23 

80 

58 

270 

20 

14 

.18 

58 

42 

140 

14 

7 

.12 

38 

27 

60 

9 



CONSTRUCTION  OF  THE  CIRCLE  DIAGRAM    345 

Et 
On  short-circuit  Isc  =  —         —r.  -  r  2 

X.  +  XJ^  )-5i  formula  43,  page  337,  so 

\  °2C2/    U2 

that  theoretically  the  relation  between  Et  and  Isc  in  the  above 
table  should  be  represented  by  a  straight  line.  The  actual 
relation  is  shown  in  curve  4,  Fig.  230;  the  curve  gradually  bends 
away  from  the  straight  line  due  to  the  gradual  saturation  of  the 
iron  part  of  the  leakage  path. 

The  watts  input  on  short-circuit  =1.73Et  Iwsc,it  is  also  = 
klsc2,  because  it  is  all  expended  in  copper  loss,  and  since  Et  is 
proportional  to  Isc,  see  curve  4,  therefore  Iwsc  also  is  propor- 
tional to  Isc  and  the  relation  is  plotted,  for  the  tests  in  the 
above  table,  in  curve  5. 

In  Art.  245,  it  was  shown  that  the  starting  torque  is  propor- 
tional to  n2I?2R2,  the  rotor  copper  loss,  where  72  is  the  rotor  cur- 
rent on  short-circuit,  and  since  72  is  proportional  to  7SC  which  is 

,  ..       starting  torque  .  .       , 

proportional  to  Et  therefore  -        -%  —        -  is  proportional  to 

tit 

I  sc  and  the  relation  is  plotted,  for  the  tests  in  the  above  table, 
in  curve  6. 

Curves  4,  5  and  6  are  produced  as  shown,  so  that  the  probable 

values  at  normal  voltage  of  7SC,  Iwsc,  and  —  ^—  may  be  deter- 

mined; at  440-volts  Isc  =370  amperes 
7WSC  =  150  amperes 
torque  in  Ib.  ft.  . 

—  iT~  —  \»2t 

volts 
torque  in  pounds  at  1  ft.  radius  =1.2X440  =  528, 

528X2^X900 
torque  in  synchronous  horse-power  =  --  ^7^  --  =  90 


248.  —  Construction  of  the  Circle  Diagram.  —  The  results  ob- 
tained from  the  curves  in  Fig.  230  are  to  be  used  in  order  to 
construct  the  circle  diagram,  Fig.  231,  from  which  the  charac- 
teristics of  the  motor  will  be  determined. 

1.  Locate  the   short-circuit    point.     With   o  as   center   and 
radius  7SC=370  amperes  describe  the  arc  of  a  circle;  of  the  total 
current  7SC  the   power  component  7w;sc  =  150  amperes.     These 
two  values  of  current  give  I,  the  short-circuit  point. 

2.  Locate  the  no-load  point.     At  440  volts  the  exciting  current 
=  7e=21   amperes  and  the  value  of   P  at  the  same  voltage  = 
1950  watts,  so  that  the  power  component  of  the  exciting  current 


346 


ELECTRICAL  MACHINE  DESIGN 


1950 

=  — •== — -7-7.^  =  2.54  amperes.     These  two  values  of  current  give 
1.  /o  X  44U 

the  point  Ie,  the  no-load  point. 

3.  Draw  the  circle.     The  circle  must  pass  through  the  two 
points  I  and  Ie  and  must  have  its  center  on  the  constant  loss  line. 

4.  Find  the  stator  and  rotor  copper  losses.     Of  the  total  copper 
loss  represented  by  Ip  the  part  mp  represents  the  stator  copper 
loss  and  is  determined  as  follows:     The  resistance  of  the  stator 
winding  from  terminal  to  neutral,  measured  by  direct  current  = 
0.112  ohms,  so  that  the  stator  copper  loss  on  short-circuit   = 
3702X 0.1 12X3  =46000  watts,  and  the  corresponding  power  corn- 


0  50  100         150         200         250 

Line  Current  in  Amperes 

FIG.  231.— Circle  diagram  for  a  50-h.p.,  440- volt.  3-ph.,  60-cycle,  900-syn. 
r.p.m.  induction  motor. 

46000 

ponent  of  current  =  ^TO — ~/Mn~^0  amperes  =mp. 
1.  /o  X  44U 

For  any  stator  current  oc 

the  constant  loss  =  pnX  1.73X440  watts 

the  stator  copper  loss  =  fe  X  1.73  X440  watts 
the  rotor  copper  loss  —  deX  1.73  X  440  watts 
the  mechanical  output  =  cdX  1.73X440  watts 

249.  To  Find  the  Characteristics  at  Full-load.— The  full-load 
=  50  h.  p.  and  the  value  of  cd  corresponding  to  this  output  = 

50  X  746 
— — — — -  =  49  amperes;  the  point  c  on  the  circle  is  then  found 

JL.  i  o  X  44U 

to  suit  and  the  following  values  scaled  off 
ce  =.51  amp. 
eg  =55  amp. 
oc  =62  amp; 


CONSTRUCTION  OF  THE  CIRCLE  DIAGRAM    347 

cd     49 

from  which  the  efficiency  =  —  =  ^-_  =  89  per  cent. 

eg     55 

the  power  f  actor  =  —  =—  =89  per  cent. 

cd  49 

the  actual  speed  =  syn.  speed  X      =900Xvr  =  865  r.p.m. 

C@  O-L 

r        de      2 
the  slip=  —  =  ^j  =4  per  cent. 

The  maximum  value  of  cd  =  120  amperes  so  that  the  maximum 

120X1.73X440 
horse-power  =  —     —  TA  "      -  =  122. 


The  maximum  value  of  ce  =  160  amperes  so  that  the  maximum 

160X1.73X440 
torque    in    synchronous    horse-power  =          —  „  =164  = 

about  3.25  times  full-load  torque. 

The  value  of  ml  =  87.  5  amperes  so  that  the  starting  torque 

87.5X1.73X440 
in  synchronous  horse-power  =  -       —  74fi~~  =        or  a"ou* 

1.8  times  full-load  torque,  which  checks  closely,  with  the  value 
found  by  brake  readings. 

In  plotting  test  results  it  is  advisable  to  plot  line  current  and 
terminal  volts  rather  than  current  per  phase  and  voltage  per 
phase,  because  then  the  diagram  becomes  independent  of  the 
connection,  since  three-phase  power  =  1.73  Editor  either  Y  or 
A  connection,  and  two-phase  power  =  2EtIi  for  either  star  or 
ring  connection. 


CHAPTER  XXXI 
CONSTRUCTION  OF  INDUCTION  MOTORS 

250.  Fig.  232  shows  the  type  of  construction  that  is  generally 
adopted  for  motors  up  to  200  horse-power  at  600  r.p.m.     The 
particular  machine  shown  is  a  squirrel-cage  motor. 

251.  The  Stator. — B,  the  stator  core,  is  built  up  of  laminations 
of  sheet  steel  0.014  in.   thick  which  are  separated  from  one 
another  by  layers  of  varnish  and  have  slots  E  punched  on  their 
inner  periphery  to  carry  the  stator  coils  D. 


FIG.  232. — Small  squirrel-cage  induction  motor. 

Two  kinds  of  slot  are  in  general  use  and  both  are  shown  in 
Fig.  233.  The  partially  closed  slot  is  used  for  all  rotors  and  has 
the  advantage  that  it  causes  only  a  small  reduction  in  the  air- 
gap  area;  the  open  slot  is  generally  used  for  stators  because  the 
stator  coils  are  subject  to  comparatively  high  voltages,  and  the 
open  slot  construction  allows  the  coils  to  be  fully  insulated 

348 


CONSTRUCTION  OF  INDUCTION  MOTORS       349 

before  they  are  put  into  the  machine,  it  also  allows  the  coils  to 
be  easily  and  quickly  repaired  in  case  of  breakdown. 

The  core  is  built  up  with  ventilating  segments  spaced  about 


Vent  Segment 
Open  Slot 
Partially  Closed  Slot 


FIG.  233. — Slots  and  vent  segments. 


FIG.  234. — Parts  of  an  Allis  Chalmers  Bullock  squirrel-cage  induction  motor. 

3  in.  apart;  one  segment  is  shown  at  F,  Fig.  232,  and  in 
greater  detail  in  Fig.  233,  and  consists  of  a  light  brass  casting 
which  is  riveted  to  the  adjacent  lamination  of  the  core;  the 


350  ELECTRICAL  MACHINE  DESIGN 

lamination  for  this  purpose  is  usually  made  of  0.025  in.  steel. 
The  laminations  are  clamped  tightly  between  two  cast-iron  end 
heads  C,  and  in  order  to  prevent  the  core  from  spreading  out  on 
the  inner  periphery,  tooth  supports  G,  of  strong  brass,  are  often 
placed  between  the  end  heads  and  the  core. 

The  stator  yoke  A  carries  the  stator  core  and  the  bearing  hous- 
ings N.  When  the  motor  has  to  be  mounted  on  a  wall,  or  on  a 
ceiling,  the  housings  N  must  be  rotated  through  90°  or  180° 
respectively;  this  is  necessary  because  ring  oiling  is  always  used 
for  motor  bearings,  and  the  oil  well  L  must  always  be  below  the 
shaft.  The  bearing  housings  help  to  stiffen  the  whole  machine 
and  allow  the  use  of  a  fairly  light  yoke.  The  shape  of  the  hous- 
ings, as  may  be  seen  from  Fig.  234,  is  such  that  it  is  a  simple 
matter  to  close  the  openings  between  the  arms  with  perforated 
sheet  metal  so  as  to  form  a  semi-enclosed  motor,  or  all  the  openings 
in  the  machine  with  sheet  metal  so  as  to  form  a  totally  enclosed 
motor. 

252.  The  Rotor.' — The  rotor  core  also  is  built  up  of  laminations 
of  sheet  steel,  which  are  usually  0.025  in.  thick;  the  use  of  such 
thick  sheets  is  permissible  because  the  frequency  of  the  magnetic 
flux  in  the  rotor  is  low  and  the  rotor  core  loss  is  small. 

The  core  with  its  vent  ducts  is  clamped  between  two  end 
heads  and  mounted  on  a  spider  K,  Fig.  232.  In  the  case  of 
squirrel-cage  rotors  the  depth  of  the  rotor  slot  is  usually  so  small 
that  a  tooth  support  is  not  required. 

The  rotor  bars  are  carried  in  partially  closed  slots  and  are 
connected  together  at  the  ends  by  rings  P  called  end  connectors; 
these  rings  are  usually  supported  on  fan  blades  which  are  carried 
by  the  end  heads. 

The  shaft  M  is  extra  stiff  because  the  clearance  between  the 
stator  and  rotor  is  very  small,  and  the  bearings  H  are  extra 
large  so  as  to  give  a  reasonably  long  life  to  the  wearing  surface. 

The  whole  machine  is  carried  on  slide  rails  Q,  which  are  rigidly 
fixed  to  the  foundation  and  by  sliding  the  motor  along  the  rails 
the  belt  may  be  tightened  or  slackened.  Slide  rails  are  not  used 
for  geared  or  direct-connected  motors. 

253.  Large  Motors.— Fig.  235  shows  the  type  of  construction 
for  large  motors.     Pedestal  bearings  are  used,  so  that  the  yoke 
has  to  be  extra  stiff  in  order  to  be  self-supporting.     The  stator 
coils  are  tied  to  a  wooden  coil  support  ring  R  which  is  carried  by 
brackets  attached  to  the  end  heads;  coil  supports  should  be  used 


CONSTRUCTION  OF  INDUCTION  MOTORS       351 

even  on  small  motors  if  the  coils  are  flimsy  and  liable  to  move 
due  to  vibration. 

Both  squirrel-cage  and  wound-rotor  constructions  are  shown 
in  Fig.  235  and  it  may  be  seen  that  the  same  spider  U  can  be 
used  in  either  case;  the  two  rotors  differ  in  the  number  and  size 
of  slots  and  in  the  shape  of  the  end  head.  S  is  a  band  of  steel 


FIG.   235. — Large  induction   motor;   both   squirrel-cage   and   wound-rotor 
construction  shown. 

wire  used  to  bind  down  the  rotor  coils  of  the  wound-rotor  machine 
on  to  the  coil  support  T  which  is  carried  by  the  end  heads;  this 
coil  support  acts  as  a  fan  and  helps  to  keep  the  machine  cool. 
When  the  rotor  diameter  is  greater  than '30  in.  the  rotor  core  is 
generally  built  up  of  segments  which  are  carried  by  dovetails  on 
the  rotor  spider. 


CHAPTER  XXXII 

MAGNETIZING  CURRENT  AND  NO-LOAD  LOSSES 

254.  The   E.M.F.    Equation. — The   revolving   field   generates 
e.m.fs.  in  the  stator  windings  which  are  equal  and  opposite  to 
those  applied,  therefore,  as  shown  in  Art.  148,  page  189, 

#=2.22  kZ<f)aflQ-8  volts,  for  full-pitch  windings 
where  E_  =  the  voltage  per  phase 

k  =  the  distribution  factor  from  the  table  on  page  189 
Z  =  the  conductors  in  series  per  phase 
<j>a  =  the  flux  per  pole  of  the  revolving  field 
"'/=  the  frequency  of  the  applied  e.m.f. 

so  that,  if  the  winding  of  an  induction  motor  and  also  its  operating 
voltage  and  frequency  are  known,  the  value  of  the  revolving 
field  can  be  found  from  the  above  equation. 

255.  The  Magnetizing  Current. — Diagram  A,  Fig.  236,  shows 
an  end  view  of  part  of  the  stator  of  a  three-phase  induction  motor 
which  has  twelve  slots  per  pole.     The  starts  of  the  windings  of 
the  three  phases  are  spaced  120  electrical  degrees  apart  and  are 
marked  Slt  S2  and  S3. 

Diagram  B  shows  the  value  of  the  current  in  each  phase  at 
any  instant. 

Diagram  C  shows  the  direction  of  the  current  in  each  conductor 
at  the  instant  F  and  the  corresponding  distribution  of  m.m.f. 

Diagram  D  shows  the  direction  of  the  current  in  each  con- 
ductor at  the  instant  G  and  the  corresponding  distribution 
of  m.m.f. 

It  will  be  seen  that  the  revolving  field  is  not  quite  constant  in 
value  but  varies  between  the  two  limits  shown  in  diagrams  C 
and  D.     The. average  m.m.f.,  ATav,  is  found  as  follows: 
Xl2A=  area  of  curve  in  diagram  C 
=  4.06/IBX   * 
3.567mX2/l 
3.0?>/mX2/l 
2.5&/mx2A 


28  6/mA 

352 


MAGNETIZING  CURRENT  AND  NO-LOAD  LOSSES     353 


UOOOOOOOOOOOOOO 


FIG.  236,— The  revolving  field. 


354  ELECTRICAL  MACHINE  DESIGN 

also  ATavXl2^  —   area  of  curve  in  diagram  D 

-  4.0X0.8666/mX5/l 

3.0X0.866  6/mX2/l 

2.0X0.866  67WX2A 

1.0X0.866  6/TOX2A 


27.7  blml 
therefore,  taking  the  mean  of  these  two  values 

A  Ta«  X  12;.  =  27.85  bImX 
and  ATav  =  2.32  6/w 


since  there  are  12  slots  per  pole 
=  0.273  (cond.  per  pole)  Ie 

The  value  of  ATav  can  be  found  in  a  similar  way  for  any 
number  of  slots  per  pole  and  for  both  two-  and  three-phase 
windings  and  varies  slightly  from  the  above  figure  for  different 
cases,  but  in  general  the  value  of  ATav  used  for  all  polyphase 
windings  =  0.273  (cond.  per  pole)  Ic. 

The  relation  between  the  flux  per  pole  and  the  magnetizing 
current  per  phase  is  found  from  the  formula 


-0.87  (cond.  per  pole)  IerL 


dC 

or/0  =  7^  -rtX-T^XaC  (44) 

0.87  (cond.  per  pole)     rLg 

where  I0  =  the  magnetizing  current  per  phase  (effective  value) 
<j)a  =  the  flux  per  pole  of  the  revolving  field 

r  =  the  pole-pitch  in  inches 

Lg  =  the  axial  length  of  air-gap  in  inches  and  is  used  instead 
of  Lc  because,  on  account  of  the  small  air-gap,  there 
is  little  fringing  into  the  vent  ducts 
d=  the  air-gap  clearance  in  inches 
C  =  the  Carter  coefficient,  see  Fig.  40,  page  44. 
To  allow  for  the  m.m.f.  required  to  send  the  flux  through  the 
iron  part  of  the  magnetic  circuit,  the  value  of  current  found  from 
the  last  formula  has  to  be  multiplied  by  a  factor  which  is  found 
from  the  results  of  similar  machines  that  have  already  been  tested; 
where  no  such  information  is  available  the  factor  is  taken  as  1.2. 


MAGNETIZING  CURRENT  AND  NO-LOAD  LOSSES     355 

256.  No-load  Losses. — These  losses  are  similar  to  and  are 
figured  out  in  the  same  way  as  the  no-load  losses  in  a  D.-C. 
machine. 

/  y   \  s/ 

Bearing  Friction  Loss  =  0.81  dq  ~     '  2watts 


where  d    =  the  bearing  diameter  in  inches 
I    =the  bearing  length  in  inches 
Vb  =the  rubbing  velocity  of  the  bearing  in  feet  per  minute. 

Brush  Friction. — This  loss  is  found  only  in  wound  rotor  motors; 

V 

it  is  very  small,  and  =1.25  A  Tr^  watts 

lUU 

where  A  is  the  total  brush  rubbing  surface  in  square  inches, 
Vr  is  the  rubbing  velocity  in  feet  per  minute. 

Windage  Loss. — This  loss  cannot  readily  be  separated  out  from 
the  bearing  friction  loss  so  that  its  value  is  not  known,  it  is 
generally  so  small  that  it  can  be  neglected. 

The  Iron  Loss. — The  frequency  of  the  flux  in  the  stator  teeth 
and  core  =/„  the  frequency  of  the  applied  voltage,  while  that 
in  the  rotor  teeth  and  core  =  s/u  where  s  is  the  per  cent.  slip. 

At  no-load  the  slip  is  practically  zero  so  that  the  rotor  loss  due 
to  the  main  flux  is  very  small  and  is  not  calculated. 

The  iron  loss  at  no-load  includes: 

The  hysteresis  and  eddy-current  loss  due  to  the  main  flux, 
Loss  due  to  filing  of  the  slots, 

Loss  due  to  alternating  leakage  fluxes  in  the  yoke  and  end  heads, 
Additional  loss  due  to  non-uniform  flux  distribution  in  the  core. 

In  addition  to  the  above  there  is  also  the  pulsation  loss  which 
is  peculiar  to  the  induction  motor.  In  Fig.  237,  A  shows  part  of 
a  motor  which  has  a  larger  number  of  slots  in  the  rotor  than 
in  the  stator.  It  may  be  seen  that  the  flux  density  in  the  rotor 
tooth  x  is  a  maximum  while  that  in  the  tooth  y  is  a  minimum, 
so  that  there  is  a  pulsation  of  flux  in  the  rotor  teeth  which  goes 
through  one  cycle  while  the  rotor  passes  through  the  distance  of 
one  stator  slot,  or  the  frequency  of  this  pulsating  flux  =  the 
number  of  stator  slots  X  the  revolutions  per  second  of  the  rotor 

In  the  same  way  there  is  a  pulsation  of  flux  in  the  stator  teeth 
with  a  frequency  =  the  number  of  rotor  teeth  X  the  revolutions 
per  second  of  the  rotor. 

These  frequencies  are  of  the  order  of  1000  cycles  per  second, 
and,  therefore,  the  loss  due  to  these  pulsations  of  flux  is  large; 


356 


ELECTRICAL  MACHINE  DESIGN 


the  tests  plotted  in  Fig.  238  give  some  idea  of  their  value.  The 
machine  on  which  the  tests  were  made  was  a  60-cycle,  wound- 
rotor  motor.  Curve  I  shows  the  loss  with  the  rotor  circuit  open 
and  therefore  the  machine  at  a  standstill,  the  rotor  current 
zero,  the  stator  current  being  the  exciting  current,  and  the  fre- 
quency of  the  flux  in  the  rotor  core  the  same  as  that  in  the 
stator  core,  then  the  loss  ab  at  any  voltage  =  the  hysteresis  and 
eddy-current  loss  due  to  the  main  field  in  both  stator  and  rotor. 
Curve  2  shows  the  loss  with  the  rotor  circuit  closed  and  the 


JliWUL 


FIG.  237. — Flux   pulsation  in 
the  rotor  teeth. 


1234 
Kilowatt  Loss 

FIG.  238. — Iron  loss  tests  on  a  3- 
phase,  60-cycle,  wound-rotor  induc- 
tion motor. 


motor  running  idle  at  synchronous  speed.  In  this  case  the  rotor 
core  loss  due  to  the  main  field  is  zero  and  the  loss  cd  at  the  same 
voltage  as  before  is  the  hysteresis  and  eddy-current  loss  in  stator 
only  and  also  the  pulsation  loss:  the  pulsation  loss  is  about  50  per 
cent,  of  the  total  no-load  loss. 

257.  Rotor  Slot  Design.- — To  make  the  pulsation  loss  a  mini- 
mum the  reluctance  of  the  air-gap  under  each  tooth  should 
remain  constant.  This  can  be  accomplished  by  the  use  of  totally 
closed  slots  for  both  rotor  and  stator;  even  partially  closed  slots 
will  give  approximately  this  result  if  the  slits  at  the  top  of  the 
slots  be  made  narrow. 

When  open  slots  are  used  in  the  stator  the  size  of  rotor  tooth 
which  makes  the  pulsation  loss  a  minimum  is  found  in  the  follow- 


MAGNETIZING  CURRENT  AND  NO-LOAD  LOSSES     357 

ing  way:  The  rotor  slot  is  made  partially  closed  and  the  rotor 
tooth  is  made  equal  to  the  stator  slot  pitch  as  shown  in  B,  Fig. 
237,  'where  it  will  be  seen  that  the  pulsation  of  flux  in  a  rotor 
tooth  is  zero  because  the  area  of  air  gap  under  a  rotor  tooth 
=  a  +  b  =  &  constant.  The  pulsation  of  flux  in  the  stator  teeth 
is  small  because  the  rotor  slots  are  almost  closed  and  the  fringing 
makes  them  equivalent  to  totally  closed  slots  so  far  as  pulsation 
is  concerned. 

258.  Calculation  of  the  Iron  Loss. — Due  to  all  the  additional 
losses  the  calculation  of  the  total  iron  loss  is  exceedingly  difficult 
and  is  usually  carried  out  by  the  help  of  the  curves  in  Fig.  81, 
page  102,  which  curves  are  found  to  apply  to  induction  motors 
as  well  as  to  D.-C.  machines.     The  value  so  found  is  approxi- 
mately correct  for  machines  with  open  stator  slots  and  partially 
closed  rotor  slots.     When  partially  closed  slots  are  used  for  both 
stator  and  rotor  the  value  found  from  the  curves  is  about  50 
per  cent,  too  large.     Where  the  number  of  slots  is  larger  in  the 
rotor  than  in  the  stator,  and  where  the  stator  slots  are  open  so 
that  the  pulsation  loss  must  be  large,  the  value  of  iron  loss  found 
from  the  curve  will  probably  be  too  small. 

259.  Calculation  of  Magnetizing  Current,  Core  Loss  and  Bear- 
ing Friction. 

A  50-h.  p.,  440- volt,  three-phase,  60-cycle,  900-syn.  r.p.m.  induction  motor 
is  built  as  follows: 

Stator  Rotor 

External  diameter 25  in.  18.94  in. 

Internal  diameter 19  in.  15.5  in. 

Frame  length 6.375  in.  6.375  in. 

Vent  ducts 1-3/8  in.  1-3/8  in. 

Gross  iron 6  in.  6  in. 

Slots,  number 96  79 

Slots,  size 0.32  in. XI. 5  in.  0.45  in. X 0.4  in. 

Cond.  per  slot,  number 6  1 

Cond.  per  slot,  size 0.14  in.  X  0.2  in.  0.4  in.  X  0.35  in. 

Connection Y  Squirrel  cage 

Air-gap  clearance 0  .03  in. 

A  stator  and  rotor  slot  are  shown  to  scale  in  Fig.  242. 

440 
The  voltage  per  phase  =  -=~  =  254  since  the  connection  is  Y. 

J.  •  /  O 

The  flux  per  pole  is  found  from  the  formula 
#  =  2.22  kZ$af  10~8,  see  page  352, 

therefore  254=2.22X0.96X  (^X^)  X<£oX60XlO~s 
from  which  00  =  1,040,000. 


358  ELECTRICAL  MACHINE  DESIGN 

Cl  the  stator  Carter  coefficient  is  found  as  follows: 


/=0.33  from  Fig.  40,  page  44 


1 


0.302  +  0.32 


0.302  +  0.33X0.32 
<72  the  rotor  Carter  coefficient  is  found  in  the  same  way 


=  1.03 


The  pole-pitch  =  —.  —  =7.48  in. 

o 

The  magnetizing  current  70  =  ^-  =-/ —  —  X  -^r 

0.87  (cond.  per  pole)     tL, 


/=0.7 

0.68  +  0.07 
2     0.68  +  0.7X0.07 


=  17.6  amperes  for  air-gap  alone 

this  has  to  be  increased  20  per  cent,  to  allow  for  the  iron  part  of  the  magnetic 
circuit,  therefore,  the  magnetizing  current  =  17. 6  X  1.2  =  21  amperes. 

The  Flux  Densities. — Fig.  239  shows  the  flux  distribution  in  a 
four-pole  induction  motor. 


FIG.  239. — Flux  distribution  in  a  four-pole  induction  motor. 

rru  4.1,    j        v  flux  Per  Pole 

The   average   stator  tooth  density  =  —    ,,  — ^-  and 

tooth  area  per  pole 

the  maximum  tooth  density,  namely,  that  at  point  A 
=  average  tooth  density  X  „ 


MAGNETIZING  CURRENT  AND  NO-LOAD  LOSSES     359 

flux  per  pole  TT 

tooth  area  per  pole     2* 

The  tooth  area  per  pole  =  teeth  per  pole  X^X  net  iron 
=  12X0.302X5.4 
=  19.6sq.  in. 

rp,  1040000     TT 

The  maximum  tooth  density  =  —  —  r-=  —  X~ 

iy.o       & 

=  83,000  lines  per  square  inch. 
The  core  area  =  the  core  depth  X  net  iron 
=  1.5X5.4 
=  8.1  sq  in. 

The  maximum  core  density  =  the  core  density  at  B,  Fig.  239 

_  flux  per  pole 
2  X  core  area 
=  1040000 
2X8.1 

=  64,000  lines  per  square  inch. 
The   total  weight  of  stator  teeth   =761b. 

The   flux  density  in  stator  teeth   =83,000  lines  per  square  inch. 
The  corresponding  loss  per  pound   =9  watts  from  Fig.  81,  page  102. 
Therefore,  the  total  stator  tooth  loss   =  680  watts. 

This  result  is  slightly  pessimistic,  because  the  maximum  tooth  density  is 
83,000  lines  per  square  inch  only  at  the  tip  of  the  tooth  and  is  less  than 
that  further  back. 

The  total  weight  of  stator  core  =166  Ib. 

The  maximum  core  density  =64,000  lines  per  square  inch. 

The  corresponding  loss  per  pound  =  6  watts  from  Fig.  81. 
Therefore,  the  total  loss  in  the  core  =  1000  watts. 
The  total  no-load  iron  loss  =  tooth  loss  +  loss  in  core 

=  1680  watts. 
The  size  of  bearings  is  3  in.  X  9  in. 

The  loss  in  each  bearing  =  0.81  dl  (TT          2  watts,  see  page  355,  where  Vb, 


the  rubbing  velocity  at  900  r,p.m.  =700  ft.  per  minute. 
Therefore,  the  loss  in  two  bearings      =  2  X  0.81  X  3  X  9  X  (7)  1 

=  810  watts. 


CHAPTER  XXXIII 
LEAKAGE  REACTANCE 

260.  Necessity  for  an  Accurate  Formula. — To  calculate  the 
reactance  voltage  of  the  coils  undergoing   commutation  in  a 
D.-C.  machine  an  approximate  formula  is  used.     A  more  accurate 
formula  is  of  little  extra  value  because  commutation  depends  on 
so  many  other  things  such  as  brush  contacts,  shape  of  pole  tips, 
etc.,  about  the  effect  of  which  comparatively  little  is  known. 

In  the  case  of  an  alternator  20  per  cent,  error  in  the  calcula- 
tion of  the  armature  reactance  has  comparatively  little  effect 
on  the  value  of  the  regulation  determined  by  calculation  since 
the  reactance  drop  is  only  a  part  of  the  total  voltage  drop,  the 
remainder  being  due  principally  to  armature  reaction. 

In  the  case  of  an  induction  motor,  however,  the  maximum 
current  Id,  and  therefore  the  starting  torque  and  the  overload 
capacity,  depend  entirely  on  the  leakage  reactance,  as  shown  in 
formula  43,  page  337,  so  that  it  is  necessary  to  develop  a  formula 
which  will  give  this  reactance  accurately. 

261.  The  Leakage  Fields.- — The  leakage  in  an  induction  motor 
consists  of  the  end  connection  and  the  slot  leakage,  which  are 
also    found   in  alternators,  and  the  leakage  (f)z,  Fig.  240,  which 
links  the  conductors  and  passes  zig-zag  along  the  air-gap. 

Except  for  the  end-connection  leakage  these  fluxes  have  no 
separate  existence  but  form  part  of  the  total  flux  in  the  machine; 
since,  however,  the  magnetic  circuit  of  an  induction  motor 
is  not  saturated,  their  effect  may  be  considered  separately. 

262.  Reactance  Formula. — If 

(j)e  =  the  lines  of  force  that  circle  1  in.  length  of  the  belt  of  end 

connections  for  each  ampere  conductor  in  that  belt. 
(f>s  =  the  lines  of  force  that  cross  the  slots  and  circle  1  in.  length 

of  the  phase  belt  of  conductors  for  each  ampere  conductor 

in  that  belt. 
<£z=  the  lines  of  force -that  zig-zag  along  the  air-gap  and  circle 

1  in.  length  of  the  phase  belt  of  conductors  for  each  ampere 

conductor  in  that  belt. 

360 


LEAKAGE  REACTANCE 


361 


then,  just  as  in  the  case  of  the  alternator,  the  stator  reactance  per 
phase  in  ohms 

=  2xfb2c2p[(j)eLe  +  (<f>8  +(f)z)Lg]lO~s  for  a  chain  winding 

=  27r/62c2p[%r^4-  (0«  +  <?yLp]10-8  for  a  double-layer  winding; 


Stator 


Rotor 


FIG.  240.— The  leakage  fields. 

because  of  its  lower  reactance  the  double-layer  winding  is  largely 
used  for  induction-motor  work. 

263.  Zig-zag  Reactance.1 — Fig.  240  shows  part  of  the  winding 
of  one  phase  of  the  stator  and  the  corresponding  part  of  the 


FIG.  241. — Zig-zag  leakage. 

rotor  winding  of  a  three-phase  induction  motor.  It  was  shown 
in  Art.  237,  page  332,  that  the  m.m.f.  of  the  rotor  is  opposed  to 
and  practically  equal  to  that  of  the  stator,  so  that  the  direction 
of  the  currents  in  the  conductor?  is  as  shown  by  the  crosses  and 
1  Adams,  Trans,  of  A.  I.  E.  E.,  Vol.  24,  page  327. 


362  ELECTRICAL  MACHINE  DESIGN 

dots  at  the  bottom  of  the  slots,  and  a  peculiar  magnetic  circuit 
is  produced  of  which  the  electrical  equivalent  is  shown  in  diagram 
A,  Fig.  240. 

The  m.m.f.  between  e  and/=6ci  ampere-turns,  therefore  the 

,,    D      3.26ci 
flux  along  one  path  Rz  =  — ~ — 

£lz 

where  Rz  is  the  reluctance  of  one  of  the  zig-zag  paths. 

In  order  to  find  Rz  it  is  assumed  for  simplicity  that  there  are 
the  same  number  of  stator  as  of  rotor  slots  so  that  ^  =  ^2  =  ^- 
also  that 

ti  =  the  width  of  the  stator  tooth  and  its  magnetic  fringe 
t2  =  the  width  of  the  rotor  tooth  and  its  magnetic  fringe 

so  that    -~  =  Cl}  the  Carter  coefficient  for  the  stator 
h 

y  =  C.,,  the  Carter  coefficient  for  the  rotor 


then  i 


£+3 


/ 


+ 


\m-\-x     m 
=  L  ™2-"2 


IS) 


7   2cw£ 
this  value  varies  over  the  range  of  half  a  slot  pitch  between  a 

maximum  when  x  is  zero  and  zero  when  x  =  -^  —  — - [  =  m 

i     2  rw  ^^2— ^^ 

and  the  average  value  of  -~-  =  -,  I  L • , 


Lgm2 


2cm§ 

2\ 
<?  / 

/t2         8A2 

2      2/ 


LEAKAGE   REACTANCE 


363 


V  C2 
herefore,  the  leakage  flux  along  one  path  R 


and  (/)z  the  lines  per  ampere  conductor  per  1  in.  length  of  stator 
or  rotor 


since  half  the  lines  link  the  stator  coils  and  t.he  other  half  link 
the  rotor  coils. 

264.  Final  Formula  for  Reactance  .  —  For  double-layer  windings 
the  stator  reactance  per  phase 

10-8 


the  rotor  reactance  per  phase 


the  maximum  current  per  phase 

volts  per  phase 

xt+xJ£f\^ 

\  U2    2/         2 

E 

~Xbg 
where  XeQ  is  the  equivalent  reactance  per  phase  and 

^^-~  }    Lg+P^-  +    (^S+^Z)Lg        10~8 

n^p    I  2n2p      \    n2p    ] 

^:+(v^^+vii±^|Lo|1o-s  (45) 


f—  / 

,         os  +  d>z         I       o  o  /  "i 
where  — — r  = 3.2 1  ^ 


364  ELECTRICAL  MACHINE  DESIGN 

the  end-connection  reactance  in  formula  45  is  the  equivalent 
reactance  of  both  rotor  and  stator.  For  squirrel-cage  motors 
the  end-connection  reactance  of  the  rotor  may  be  neglected  and 

the  curve  for—-  -  in  Fig.  244  used  directly.     For  wound-rotor 

IV 

motors  on  the  other  hand  it  might  seem  at  first  that  this  value 
should  be  doubled,  but  it  must  be  remembered  that  the  m.m.fs. 
of  rotor  and  stator  are  opposing  and  the  leakage  flux  has  to  get 
through  the  space  Vj  Fig.  235,  between  the  two  layers  of  wind- 
ings, so  that  the  closer  together  these  windings  are  the  more 
restricted  is  the  space  V  and  the  smaller  the  leakage  flux;  for 

ordinary  motors  it  is  satisfactory  to  use  the  value  for  —  --  in 

Fig.  244  and  increase  it  by  35  per  cent. 

Example  of  Calculation.  —  Find  the  maximum  current  Id 
for  the  following  machine. 

Rating.  —  50  h.  p.,  440  volts,  three-phase,  60  cycle,  900  syn. 
r.p.m.  The  construction  of  the  machine  is  as  follows: 

Stator  Rotor 

External  diameter  ..........  25  in.  18.91  in. 

Internal  diameter  ...........  19  in.  15.5  in. 

Frame  length  ...............  6.375  in.  6.375  in. 

Vent  ducts  .................  1-3/8  in.  1-3/8  in. 

Gross  iron  .................  6  in.  6  in. 

Slots,  number  ..............  96  79 

Slots,  size  .................  0.32  in.  XI.  5  in.       0.45  in.  X  0.4  in. 

Cond.  per  slot,  number  ......  6  1 

Cond.  per  slot,  size  ..........  0.14  in.  X  0.2  in.       0.4  in.  X  0.35  in. 

Connection  .................  Y  Squirrel  cage 

Winding  ....................  Double  layer 

Air-gap  clearance  ...........  0.03  in. 

A  stator  and  a  rotor  slot  are  shown  to  scale  in  Fig.  242. 
The  calculation  is  carried  out  in  the  following  way: 
pole-pitch  =7.5  in. 

^p  =  4.3  from  Fig.  244 
=  0.622 


(7,  =  1.52 
£,-1.03 


nlP    ~96_        \3X0 

=       [6.3  +  2.1]  for  the  stator 


1-3      ,  °-2  \  ,  Q  26°-62V    l     1     l 
0.32+0.32/+      '°0.03     1.52  +  1.03 


LEAKAGE  REACTANCE  365 

0-26  0^03  \L52  +  UM~l)  J 


l  fc  0/0.40          2X0.07 
79  3X0.45  ^ 


=     r  [3.2  +  2.6]  for  the  rotor 


=  0.415(0.54  +  0.96) 
=  0.62  ohms 

440 
The  voltage  per  phase =^-^  =  254  since  the  connection  is  Y  and  the  maxi- 

254 
mum  current  per  phase  =  ^—^  =  410  amperes. 


<— 6.32^ 


L0.03 


FIG.  242. — Stator  and  rotor  slot  for  a  50-h.p  900-syn.  r.p.m.  induction 

motor. 

265.  Belt  Leakage.1 — In  addition  to  the  end  connection,  slot, 
and  zig-zag  leakage,  there  is  another  which  enters  into  the  react- 
ance formula  for  a  wound -rotor  motor,  namely,  the  belt  leakage. 

In  developing  the  formula  on  page  363  it  was  assumed  that 
the  m.m.f.  of  the  rotor  was  equal  and  opposite  to  that  of  the 
stator  at  every  instant.  This  cannot  be  the  case  in  a  wound- 
rotor  machine  because,  as  shown  in  Fig.  221,  the  winding  is 
arranged  in  phase  belts  and  the  stator  and  rotor  belts  sometimes 
overlap  one  another. 

When  the  stator  and  rotor  are  in  the  relative  position  shown  in 
diagram  A,  Fig.  243,  the  currents  in  the  stator  phase  belts  are 

1  Adams,  Trans,  of  International  Electrical  Congress,  1904,  Vol.  1,  page 
706. 


366 


ELECTRICAL  MACHINE  DESIGN 


exactly  opposed  by  those  in  the  rotor  phase  belts.  The  starts 
of  the  windings  of  the  three  phases  are  spaced  120  electrical 
degrees  apart,  and  it  may  be  seen  from  diagram  A,  that  the  cur- 
rents in  the  three  stator  belts  S1}  S2  and  S3,  and  also  in  the  three 
rotor  belts  R1}  R?  and  R3  are  out  of  phase  with  one  another 
by  60  degrees;  they  are  represented  by  vectors  in  diagram  B. 

When  the  stator  and  rotor  are  in  the  relative  position  shown 
in  diagram  C  the  currents  in  the  belts  have  the  phase  relation 
shewn  in  diagram  D. 


s\ 


s. 


fr"^*  nnonoooOQI 


FIG.  243. — Belt  leakage  in  3-phase  machines. 

Part  of  diagram  C  is  shown  to  a  large  scale  in  diagram  E 
where  it  may  be  seen  that  belt  R3  overlaps  belt  S3  by  a  distance 
fg  and  belt  S2  by  a  distance  gh. 

In  the  belt  fg  the  current  in  the  stator  conductors  is  S'3, 
diagram  D,  and  that  in  the  rotor  conductors  is  R?,  of  which  the 
component  om  opposes  the  stator  current;  mn,  the  remaining 
part  of  the  stator  current,  is  not  opposed  by  an  equivalent  rotor 
current  and  is  represented  by  crosses  in  diagram  E. 

In  the  belt  gh  the  current  in  the  stator  conductors  is  S2,  dia- 


LEAKAGE  REACTANCE  367 

gram  D,  and  that  in  the  rotor  conductors  is  R3,  of  which  the 
component  op  opposes  the  stator  current;  pq,  the  remaining  part 
of  the  stator  current,  is  not  opposed  by  an  equivalent  rotor  cur- 
rent and  is  represented  by  dots  in  diagram  E. 

The  currents  represented  by  crosses  and  dots  in  diagram  E  set 
up  the  flux  (f>b,  which  is  in  phase  with  the  belt  of  conductors 
which  it  links  and  is  therefore  the  same  in  effect  as  a  leakage 
flux;  it  is  called  the  belt  leakage.  </>&  varies  through  one  cycle 
while  the  rotor  moves,  relative  to  the  stator,  through  the  dis- 
tance of  one-phase  belt,  and  this  belt  flux  is  the  cause  of  the 
variation  in  short-circuit  current  with  constant  applied  voltage 
that  is  found  in  wound  rotor  motors,  when  the  rotor  is  moved 
relative  to  the  stator. 

The  belt  flux  per  ampere  conductor  in  the  phase  belt  and  per 
inch  axial  length  of  core  depends  on  the  reluctance  of  the  belt- 
leakage  path  and  is  directly  proportional  to  the  pole-pitch,  in- 
inversely  proportional  to  the  air-gap  clearance  and  to  the  Carter 
fringing  constant,  and  is  the  greater  the  smaller  the  number  of 
phases  and  therefore  the  wider  the  phase  belt,  so  that  the 
average  value  of  the  belt  leakage  that  circles  1  in.  length  of  the 
phase  belt  per  ampere  conductor  in  that  belt, 

=  a  const.   X 


and  the  average  belt  reactance  per  phase  which  must  be  added 
to  formula  45,  page  363,  in  the  case  of  wound-rotor  motors 


const.  X  (46) 


In  addition  to  varying  with  the  number  of  phases,  the  constant 
depends  on  the  number  of  slots  per  phase  per  pole  because,  as 
shown  in  diagram  E,  the  belt  flux  which  links  conductors  a  and 
b  is  smaller  than  if  these  conductors  were  concentrated  in  slot  c. 
The  value  of  the  constant,  which  is  found  theoretically,  is  given 
in  the  following  table: 

Stator  slots  per  pole  Two-phase  motors  Three-phase  motors 

6  0.0052X3  0.00107X3 

12  XI.  5  XI.  5 

18  XI.  25  Xl-25 

24  XI.  15  XI.  15 

30  X  1  .  10  X  1  .  1 

Infinity.  Xl.O  Xl.O 


368 


ELECTRICAL  MACHINE  DESIGN 


For  motors  which  have  two-phase  stators  and  three-phase 
rotors  a  mean  value  should  be  used. 

266.  Approximate  Values  for  the  Leakage  Reactance. — For  a 
machine  with  a  double-layer  winding  the  equivalent  reactance 
per  phase 

-'    from    for- 


mula  45,  page  363,  where 

6  L 

~—  varies  with  the  pole-pitch  as  shown  in  Fig.  244. 

2.0 


4  6  8  10  12 

Pole  Pitch  in  Inches 
FIG.  244. — Leakage  constants. 


smce 


14 


16  18 


'  the  total  slot 


width  per  pole,  is  proportional  to  the  pole-pitch,  therefore  — 
is  approximately  inversely  proportional  to  the  pole-pitch. 

=  ~~       "  ^s    approximately 


LEAKAGE  REACTANCE 


369 


constant,  the  maximum  value  being  limited  by  humming  as 
shown  in  Art.  282,  page  387,  and  that  being  the  case  the 
Carter  fringing  constants  Cl  and  C2  are  also  approximately 
constant.  The  number  of  slots  per  pole  =nXc  is  approx- 
imately proportional  to  the  pole-pitch,  therefore  —  is 

approximately  inversely  proportional  to  pole-pitch. 
The  reactance  per  phase  then 

=  27rfb2c2pn(Kl  +  K2Lg)W-s  (47) 

where  K^  and  K2  are  plotted  in  Fig.  244  against  pole-pitch,  from 
the  results  of  tests  on  a  large  number  of  machines  with  open 


16 


14 


12 


10 


12345678 
Values  of  Lg  in  Inches 

FIG.  245. — Variation  of  the  leakage  flux  with  frame  length. 


stator  slots,  partially  closed  rotor  flots,  and  double-layer  wind- 
ings. The  reason  for  the  large  value  for  wound-rotor  motors 
compared  with  that  for  squirrel-cage  machines  is  that  in  the 
former  there  is  the  additional  end-connection  leakage  of  the 
rotor,  the  belt  leakage,  and  the  larger  rotor-slot  leakage  due  to 
the  deep  slots  required  to  accommodate  the  rotor  conductors  and 
insulation. 

The  method  whereby  these  constants  were  determined  may  be 
understood  from  the  following  example.  ^ 

24 


370  ELECTRICAL  MACHINE  DESIGN 

Three  machines  were  built  as  follows: 


A 

B 

C 

Terminal  voltage  

440 

440 

440 

Phases  

3 

3 

3 

Cycles  

60 

60 

60 

Poles  

8 

8 

8 

Stator  internal  diameter  . 

19  in. 

19  in. 

19  in 

Pole-pitch  

7.5  in. 

7.5  in. 

7.5  in. 

Gross  iron  

.     4.5  in. 

6  in. 

7.75  in. 

Slots  per  pole  

12 

12 

12 

Conductors  per  slot  

.  .  8 

6 

8 

Connection  

Y 

Y 

A 

Maximum  current  Id  ^v*. 

a  tc-oc...    270 

400 

575 

The  results  are  worked 

up  as  follows: 

Voltage  per  phase 

254 

254 

440 

Current  per  phase  

.    270 

400 

334 

Reactance  per  phase  

0.94 

0.63 

1.32 

K  +K  L 

.10.2 

12.2 

14.2 

These  results  are  plotted  against  the  values  of  Lg  in  Fig.  245 
from  which  it  may  be  seen  that  Kl}  the  part  which  is  independent 
of  the  frame  length,  =4.2  while  K2  =  1.30;  these  values  check 
closely  with  the  curves  in  Fig.  244. 


CHAPTER  XXXIV 


THE  COPPER  LOSSES 

267. — Copper  Losses  in  the  Conductors. 

If  L&^the  length  of  a  stator  conductor   in  inches 
7ci  =  the  effective  current  per  conductor 
M\  =  the  section  of  each  conductor  in  cir.  mils 

then  the  resistance  of  one  conductor  =  -~  ohms; 

IvL  j 

the  loss  in  one  conductor 

and  the  total  stator  copper  loss 


=     M      WattS 

total  cond.  X  Lbl  X  /2C1 


=  £l  watts 


(48) 


Similarly  the  total  rotor  copper  loss    =  —  2  2*2  —  -  watts        (49) 

M2 

268.  The  Rotor  End  -connector  Loss.  —  Fig.  246  shows  the 
distribution  of  current  in  part  of  the  rotor  of  a  squirrel-cage 
induction  motor. 


FIG.  246. — Current  distribution  in  the  rotor  end  connectors. 

The  effective  current  in  each  rotor  bar  =/C2 
The  average  current  in  each  rotor  bar    —  T^V 

The  current  in  the  ring  at  A  =  the  maximum  current  in  the  ring 
=  average  current  per  cond.  Xl/2  (cond.  per  pole) 


2p 


371 


372  ELECTRICAL  MACHINE  DESIGN 

The  effective  current  in  each  ring  =^-^T 

1.11 

™,  .  ,  ,        ,     .  nDrXkr 

The  resistance  of  each  ring  ==  ^  x  1270000 

where  Dr  =  the  mean  diameter  of  the  ring  in  inches 
Ar  =  the  area  of  the  ring  in  square  inches 
A  rX  1,270,000  =  the  area  of  the  ring  in  cir.  mils 
_  the  specific  resistance  of  the  ring  material 
the  specific  resistance  of  copper 

' 


The  loss  in  two  rings  =3X         jx  x 


In  addition  to  the  above  copper  losses  there  are  eddy-current 
losses  in  the  conductors  due  to  the  leakage  flux  which  crosses  the 
slot  horizontally,  as  described  in  Art.  189,  page  248.  To  prevent 
these  losses  from  having  a  large  value  it  is  necessary  to  laminate 
the  conductors  horizontally. 

When  the  rotor  is  running  at  full  speed  the  eddy-current  loss 
in  the  rotor  bars  is  small,  because  the  rotor  frequency  is  low; 
even  at  standstill,  when  the  rotor  frequency  is  the  same  as  that 
of  the  stator,  the  eddy-current  loss  in  the  rotor  bars  is  still  low 
because  the  conductors  are  not  very  deep. 

Such  eddy-current  loss  at  standstill  causes  an  increase  in  the 
starting  torque  without  a  sacrifice  of  the  running  efficiency,  since 
the  frequency  is  low  and  the  eddy  current  loss  negligible  at  full- 
load  speed.  A  number  of  patents  have  been  taken  out  on 
different  methods  of  exaggerating  this  eddy-current  loss  in  the 
rotor,  but  motors  built  under  these  patents  have  not  come  into 
general  use.  * 

EXAMPLE  OF  COPPER  Loss  CALCULATION 

A  50-h.  p.,  440-volt,  3-phase,  60-cycle,  900-syn.  r.p.m.  induc- 
tion motor  is  built  as  follows: 

Stator  Rotor 

External  diameter  ..........  25  in.  18.94  in. 

Internal  diameter  ...........  19  in.  15.5  in. 

Frame  length  ...............   6  .  375  in.  6  .  375  in. 

Slots,  number  ..............  96  79 


THE  COPPER  LOSSES 


373 


Slots,    size 0 . 32  in.  X  1 . 5  in.    0 . 45  in.  X  0.4  in. 

Cond.  per  slot,  number 6  1 

size 0. 14  in. X 0.2  in.    0.4  in. X 0.35  in. 

Connection Y  Squirrel  cage 

Section  of  each  end  ring,  A  f .  .   0 . 75  sq.  in. 
Mean  diameter  of  end  rings .  .17.5  in. 
Resistance  of  end-ring  material  is  5  times  that  of  copper. 
The  circle  diagram  for  the  machine  is  shown  in  Fig.  247;  it  is  required 
to  draw  in  the  copper  loss  lines. 


FIG.  247. — Calculated  circle  diagram  for  a  50-h.p.,  440-volt,  3-phase,  60- 
cycle,  900-syn.  r.p.m.  induction  motor. 


L&!  the  length  of  stator  conductor 
Lfo  the  length  of  rotor  conductor 

The  maximum  stator  current  per  cond. 


The  maximum  rotor  current  per  conductor  =  (415  — 21)  X 


=  20.5  in,,  from  Fig.  84 
=  frame  length +  4  in. 
=  10.5  in. 

=  the  maximum  current  in  the 
line,  since  the  connection  is  Y 
=  415  amp. 

96X6 


79 


=  394X 


96X6 


The  maximum  stator  cond.  loss 


The  maximum  rotor  cond.  loss 


The  maximum  rotor  ring  loss 


79 

2880  amp. 
96X6X20.5X4152 
0.14X0.2X1270000" 

From  formula  48. 
57  kw. 

79X1X10.5X28802 
0.4X0.35X1270000 

From  formula  49. 
39  kw. 

9X2880\2     17.5X5 
1000X8  /    'x    0.76" 

From  formula  50 . 
=  47  kw. 


-fi 


374  ELECTRICAL  MACHINE  DESIGN 

Therefore  in  Fig.  247 

1. 73  X  440  Xab=  57,000 

and  a&  =  75  amp. 

1. 73  X  440  X  6c  =  39,000 

and  be  =  51  amp. 

1. 73  X  440  Xcd  =  47,000 

and  cd  =  Q2  amp. 

From  these   figures   the   loss  lines  can  readily  be  drawn  in.     The  final 
circle  compares  closely  with  that  found  from  test  and  plotted  in  Fig.  231. 


CHAPTER  XXXV 
HEATING  OF  INDUCTION   MOTORS 

269.  Heating  and  Cooling  Curves. — The  losses  in  an  electrical 
machine  are  transformed  into  heat;  part  of  this  heat  is  dissipated 
by  the  machine  and  the  remainder,  being  absorbed,  causes  the 
temperature  of  the  machine  to  increase.  The  temperature 
becomes  stationary  when  the  heat  absorption  becomes  zero, 
that  is,  when  the  point  is  reached  where  the  rate  at  which  heat 
is  generated  in  the  machine  is  equal  to  the  rate  at  which  it  is 
dissipated  by  the  machine. 


A 


\ 


-de 


Time  in  Seconds 

FIG.  248. — Heating  and  cooling  curves. 


The  rate  at  which  heat  is  dissipated  by  any  machine  depends 
on  8,  the  difference  between  the  temperature  of  the  machine 
and  that  of  the  surrounding  air.  During  the  first  interval  after 
a  machine  has  been  started  up,  S  is  small,  very  little  of  the 
generated  heat  is  dissipated,  therefore  a  large  part  is  absorbed 
and  the  temperature  rises  rapidly.  As  the  temperature  increases, 
that  part  of  the  heat  which  is  dissipated  increases,  therefore  the 
part  which  is  absorbed  decreases  and  the  temperature  rises  more 
slowly.  The  relation  between  temperature  rise  and  time  is 
shown  in  Fig.  248.  The  equation  to  this  curve  is  derived  as 
follows : 

375 


376  ELECTRICAL  MACHINE  DESIGN 

In  a  given  machine  let  d8  be  the  increase  in  temperature  in  the 
time  dt. 

The  heat  generated  during  this  time  =QXdt  Ib.  calories 
where  Q  =  0.53(kw.  loss) 

The  heat  absorbed  by  the  machine  =WXsXd8  Ib.  calories 
where  W  is  the  weight  of  the  active  part  of  the  machine  in  pounds 

and  Sj  its  specific  heat  =0.1  approximately 
The  heat  dissipated  =A(a  +  bV)8xdt  Ib.  calories 
where  A  is  the  radiating  surface  of  the  machine 
V  is  the  peripheral  velocity 
a  and  b  are  constants. 

The  heat  generated  =  the  heat  dissipated  +  the  heat  absorbed 
or 


and  the  temperature  rise  is  a  maximum  and  =  8m  when  the  heat 
absorbed  is  zero  or  when 

Qdt=A(a+bV)8mdt 
therefore 

A(a+bV)8mdt=A(a+bV)8dt  +  Wsd8 

Wsd8 


and 


>-  f 

o          Jo 


t  i.-  v.  -  Ws 

from  which 


A(a+bV) 

and  s^8  =  e~A~^^~ 

therefore  8  =  8  m  1 1  —  e         W^ 


=  8m(l-e-T)  (51) 


•   ,  Ws 

where  T  = 


A(a+bV} 

Ws8m 

A(a+bV)6, 


Q 
or  QT  =  Ws8m  (52) 


HEATING  OF  INDUCTION  MOTORS  377 


Therefore  T  is  the  time  that  would  be  taken  to  raise  the  tem- 
perature of  the  machine  6m  deg.  if  all  the  heat  were  absorbed. 

The  cooling  curve  is  the  reciprocal  of  the  heating  curve  and  its 
equation  is  derived  as  follows: 
if  the  temperature  falls  d®  deg.  in  dt  seconds  then 
the  heat  dissipated  =  -  WXsXdS  =  A(a  +  bV)S  Xdt 

Ws       dS 


therefore  dt=  — 


A(a+bV)    8 


and 


from  which  6  =  9me~~  (53) 


If  the  motor  is  standing  still  while  cooling  the  temperature 
drops  much  more  slowly,  as  shown  in  Fig.  249. 

Consider  the  following  example:  An  induction  motor  is  run 
at  full  load  and  the  final  temperature  rise  =45°  C. 
The  current  density  in  the  stator  cond.  =480  cir.  mils  per  ampere 
The  iron  loss  at  no-load  and  normal  voltage  =  1000  watts 
The  weight  of  iron  in  the  stator  =115  Ib. 
The  iron  loss  per  pound  =8.7  watts 
It  is  required  to  find  the  time  constant  T. 

The  resistance  of  a  copper  wire  L  in.  long  and  M  cir.  mils 
section 

=  1r-r  ohms. 
M 

The  loss  in  this  wire  due  to  a  current  / 

=  -Tur  watts 
M 

=  —  —  X5.3X10"4  Ib.  calories  per  second. 

The  weight  of  this  wire  =  LxMx2.5XlO~7  Ib. 
The  specific  heat  of  copper  =0.09. 
Since  QT  =  WsSm 


therefore          X5.3X10  ~4X  T  =  LXMx2.5XlO  -?X0.09X  0TO 
M 

Sm  2.3  XlO4 

and  -rfr  =  7—-  --  M  —  —  ^  deg.  Cent,  rise  per  second. 

T      (cir.  mils  per  amp.)2 


378 


ELECTRICAL  MACHINE  DESIGN 


In  the  given  problem      M  =  480  and  6>m  =  45°  C. 
therefore  T  for  the  coils      =450  seconds. 

Consider  now  the  iron  loss: 
The  loss  per  pound  of  iron  =P  watts 

=  PX5.3X10~4      Ib.     calories 

second 
The  specific    heat  of    iron  =0.1  approximately 

Since  QT  =  Ws0m 

therefore  PX5.3X  10~4X  T  =  l  XO.l  X  9m 


per 


~     =  T7  deg.  Cent,  rise  per  second. 


and 


In  the  given  problem  P  =  8.7  watts  per  pound  and  $m  = 
therefore  T  for  the  iron  of  the  stator  =1000  seconds. 


C. 


20  40 


GO 


D  100  120  140  160  180          200 

Time  in  Minutes 


FIG.  249. — Heating  and  cooling  curves. 


For  the  value  of  T  found  for  the  copper,  and  for  $w  =  47°  C., 
the  relation  between  temperature  and  time  is  plotted  in  Fig. 
249,  and  it  will  be  seen  that  the  calculated  curve  differs  consider- 
ably from  that  found  from  test. 

The  actual  temperature  rise  in  a  given  time  is  less  than  that 
calculated  because:— 

a.  It  has  been  assumed  that  all  the  iron  loss  is  in  the  stator 
whereas  a  portion  of  it  which  cannot  readily  be  separated  out  is 
due  to  rotor  pulsation  loss. 

b.  Part  of  the  heat  developed  in  the  active  part  of  the  machine 
is  conducted  to  and  absorbed  by  the  frame. 


HEATING  OF  INDUCTION  MOTORS  379 

c.  The  temperature  of  the  copper  rises  more  rapidly  than  that 
of  the  iron  and  there  is.  a  transfer  of  heat  which  tends  to  bring 
them  to  the  same  temperature. 

d.  The  thermal  capacity  of  the  insulation  has  been  neglected. 

270.  Time   to   Reach   the   Final   Temperature. — Due   to    the 
chances  of  error  pointed  out  above  it  is  difficult  to  predetermine 
the  rate  of  increase  of  temperature. 

It  may  be  seen  from  formula  51  that  the  larger  the  value  of 
T,  which  is  called  the  time  constant,  the  smaller  is  the  rate  of 
increase  of  temperature.  T  is  the  time  that  would  be  taken  to 
raise  the  temperature  of  the  machine  to  its  final  value  if  all  the 
heat  were  absorbed,  so  that  the  lower  the  copper  and  iron 
densities  the  larger  the  value  of  T  and  the  smaller  the  rate  of 
increase  of  temperature. 

Slow-speed  machines  have  poor  ventilation  and  therefore  low 
copper  densities  so  that  for  such  machines  the  rate  of  increase 
of  temperature  is  comparatively  small. 

Low-frequency  machines,  in  which  the  flux  density  in  the  core 
is  limited  by  permeability  rather  than  by  the  iron  loss,  have  the 
loss  per  pound  of  iron  low  and  the  rate  of  increase  of  temperature 
comparatively  small. 

The  current  density  in  the  field  coils  of  D.-C.  machines  is 
usually  of  the  order  of  1200  cir.  mils  per  ampere  so  that  such 
coils  heat  up  slowly. 

271.  Intermittent  Ratings. — Suppose  that  a  motor  is  operating 
on  a  continuous  cycle,  X  seconds  loaded  and  Y  seconds  without 
load,  the  final  temperature  will  vary,  during  each  cycle,  between 
9X  and  Syj  Fig.  248,  where  these  temperatures  are  such  that  the 
temperature  increase  in  time   X  is  equal  to  the  temperature 
decrease  in  time  Y.     Under  such  conditions  of  service  therefore 
Syj  the  highest  temperature,  is  lower  than  &„,,  the  maximum 
temperature  which  would  be  obtained  on  continuous  operation 
under  load.     For  such  service,  therefore,   a  motor  may  have 
higher  copper  and  iron  densities  than  it  would  have  if  designed 
for  the  same  load  but  for  continuous  operation. 

272  Heating  of  Squirrel -cage  Motors  at  Starting. — The  loss 
in  a  squirrel-cage  rotor  at  starting  is  very  large  and  equals  the 
full-load  output  of  the  machine  X  the  per  cent,  of  full-load  torque 
required  to  start  the  load.  Thus,  if  a  20  h.  p.  squirrel-cage  motor 
has  to  develop  full-load  torque  at  starting  the  rotor  loss  under 
these  conditions  must  be  20  h.  p.  This  loss,  in  the  form  of  heat, 


380  ELECTRICAL  MACHINE  DESIGN 

has  to  be  absorbed  by  the  rotor  copper,  and  the  temperature 
rises  rapidly  unless  there  is  sufficient  body  of  copper  to  absorb 
this  heat  during  the  starting  period. 

The  stator  current  also  is  large  at  starting;  an  average  squirrel- 
cage  motor  with  normal  voltage  applied  to  the  terminals  develops 
about  1.5  times  full-load  torque  and  takes  about  5.5  times  full- 
load  current;  when  started  on  reduced  voltage  it  develops  full- 
load  torque  with  about  4.5  times  full-load  current,  since  the 
starting  torque  is  proportional  to  the  rotor  loss  and  therefore 
to  the  square  of  the  current. 

As  shown  in  Art.  269,  the  temperature  rise  when  the  heat  is  all 
absorbed  may  be  found  from  the  following  formula. 

2.3  XlO4 

Degrees  Cent,  rise  per  sec.  =—.  --  ^  —  —=  for  copper  wire 

(cir.  mils  per  amp.)2 

watts  per  Ib.  .      .        ,     ,. 
1  q  —   -  for  iron  bodies 


watts  per  Ib.  .  ,. 

—  y^x  —  -  for  copper  bodies. 


An  average  value  for  the  cir.  mils  per  ampere  at  full-load  is 
500,  for  both  rotor  and  stator.  The  starting  current  in  the  motor 
for  full-load  torque  is  about  4.5  times  full-load  current,  the 
corresponding  value  of  cir.  mils  per  ampere  is  110,  and  the  tem- 
perature rise  1.9°  C.  per  second. 

The  proper  weight  of  end  connector  to  be  used  in  any  par- 
ticular case  depends  on  the  starting  torque  required  and  the 
time  needed  to  bring  the  motor  up  to  full  speed.  For  motors 
from  5  h.  p.  to  100  h.  p.  the  loss  per  pound  of  end  connector  is 
generally  taken  about  1  kw.  and,  corresponding  to  this  loss, 
the  temperature  rise  of  the  end  connectors 

1000 


=  6°  C.  per  second  approximately. 

273.  Stator  Heating.  —  The  temperature  rise  of  the  stator  of  an 
induction  motor  is  fixed  in  the  same  way  as  that  of  the  armature 
of  a  D.-C.  machine. 

For  induction  motors  built  with  iron  of  the  same  grade  as  used 
in  D.-C.  machines  and  of  a  thickness  of  0.014  in.,  so  that  the  iron 
loss  curves  are  as  shown  in  Fig.  81,  the  following  flux  densities 


HEATING  OF  INDUCTION  MOTORS  381 

may  be  used  for  a  machine  whose  temperature  rise  at  normal 
load  must  not  exceed  40°  C. 

Maximum  tooth  density    Maximum  core  density  in 
frequency  .    ,.  .  ,. 

in  lines  per  sq.  in.  lines  per  sq.  in. 

60  cycles  85,000  65,000 

25  cycles  100,000  85,000 

These  figures  represent  standard  practice  for  machines  with  open 
stator  slots  and  partially  closed  rotor  slots  when  the  rotor  slot 
is  designed  as  pointed  out  in  Art.  257,  page  356,  for  minimum 
pulsation  loss.  When  both  stator  and  rotor  slots  are  partially 
closed  these  densities  may  safely  be  increased  15  per  cent. 
The  end  connection  heating  is  limited  by  keeping  the  value  of 

.     amp.  cond.  per  inch  .  . 

the  ratio  — ^- — ^ —  below  that  given    in   Fig.   250, 

cir.  mils  per  amp. 

which  curve  applies  to  wound-rotor  motors,  and  to  squirrel-cage 
motors  with  less  than  4  per  cent,  slip,  of  the  type  shown  in 
Figs.  232  and  235. 

274.  Rotor  Heating. — At  full-load  and  normal  speed  the  fre- 
quency of  the  flux  in  the  rotor  is  very  low  so  that  comparatively 
high  flux  densities  may  be  used.     The  rotor  tooth  density  is  not 
carried  above  120,000  lines  per  square  inch  if  possible,  because, 
for  greater  values,  the  m.m.f.  required  to  send  the  flux  through 
these  teeth  becomes  large  and  causes  the  power  factor  to  be  low; 
for  the  same  reason  the  rotor  core  density  is  seldom  carried  above 
the  point  of  saturation,  namely  about  85,000  lines  per  square 
inch.     So  far  as  heating  is  concerned  the  rotor  core  loss  is  so 
small  that  it  may  be  neglected. 

The    rotor    copper    loss    is    limited    by    making    the    ratio 

amp.  cond.  per  inch  e       .  .       . 

— ~  — ^ —  -  the  same  for  the  rotor  as  for  the  stator,  and 

cir.  mils  per  amp. 

then,  if  the  motor  is  of  the  squirrel-cage  type,  any  additional 
rotor  resistance  that  is  required  to  give  the  necessary  starting 
torque  is  put  in  the  end  connectors,  which  are  easily  cooled. 

Since  the  rotor  ventilation  is  better  than  that  of  the  stator, 
because  it  is  revolving,  the  rotor  temperature  is  generally  lower 
than  that  of  the  stator  and  is  not  calculated. 

275.  Effect  of  Rotor  Loss  on  Stator  Heating. — The  heating  of 
the  rotor  causes  the  air  which  blows  on  the  stator  to  be  hotter 
than  the  surrounding  air.     The  heating  curve  in  Fig.  250  applies 
to  squirrel-cage  motors  with  about  4  per  cent,  slip  or  4  per  cent. 


382 


ELECTRICAL  MACHINE  DESIGN 


rotor  loss,  and  for  the  type  of  construction  shown  in  Figs.  232 
and  235.  When  greater  rotor  loss  than  this  is  required,  as  in  the 
case  of  squirrel-cage  motors  for  operating  certain  classes  of 
cement  machinery,  then  the  air  blowing  on  the  stator  will  be 
hotter  than  usual  and  the  stator  temperature  will  be  higher 
than  the  value  got  from  Fig.  250.  On  account  of  this  extra 
rotor  loss  such  high  torque  squirrel-cage  motors  are  built  on 
frames  that  are  about  20  per  cent,  larger  than  standard. 


l.Z 

i  1.0 

S 

S 

§  0.8 
3 
i 
o  0.6 

ado.4 
•^ 

H 
CD 

£0.2 

§ 

O 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

x^ 

1  2  3  4  5  6xlO; 

Peripheral  Velocity  of  Rotor  in  Ft.  per  Min. 

FIG.  250. — Heating  of  the  stator  end  connections. 


276.  Effect  of  Construction  on  Heating. — Fig.  251  shows  the 
relative  proportions  of  a  25-cycle  and  of  a  60-cycle  motor  of  the 
same  horse-power  and  speed  and  therefore  with  the  same  size 
of  bearings.     In  the  case  of  the  25-cycle  machine  the  bearing 
blocks  up  the  air  inlet,  and  in  such  a  case  the  temperature  rise 
should  be  figured  conservatively  until  the  first  machine  has  been 
tested  and  accurate  data  obtained.     Another  objection  to  the 
25-cycle  motor  is  that  the  coils  stick  out  a  considerable  distance 
from  the  iron  of  the  core  and  there  is  a  tendency  for  the  cooling 
air  to  circulate  as  shown  by  the  arrows  and  not  to  pass  out  of 
the  machine;  in  such  a  case  it  may  be  necessary  to  put  in  a  baffle, 
as   indicated    by   the  dotted  line  A,  to  deflect  the  air  stream 
in  the  proper  direction. 

277.  Heating  of  Enclosed  Motors. — Experiment  shows  that  in 
the  case  of  a  totally  enclosed  motor  the  temperature  rise  of  the 
coils  and  core  of  the  machine  is  proportional  to  the  total  loss 


HEATING  OF  INDUCTION  MOTORS 


383 


(neglecting  bearing  friction)  and  is  independent  of  the  distribu- 
tion of  this  loss,  is  inversely  proportional  to  the  external  radiating 
surface  and  depends  on  the  peripheral  velocity  of  the  rotor  in  the 
way  shown  in  Fig.  94. 


FIG.  251. — Motors  built  for  the  same  output  and  speed  but  for  different 

frequencies. 


278.  Heating  of  Semi -enclosed  Motors. — When  the  openings 
in  the  frame  of  a  motor  are  blocked  up  with  perforated  sheet 
metal  the  machine  is  said  to  be  semi-enclosed.  The  perfo- 
rated metal  acts  as  a  baffle,  prevents  the  free  circulation  of 
air  through  the  machine,  and  causes  the  temperature  to  rise,  on 
an  average,  about  25  per  cent,  higher  than  it  would  for  the  same 
machine  operating  at  the  same  load  but  as  an  open  motor. 

The  effect  of  enclosing  a  motor  may  be  seen  from  the  following 
table  which  gives  the  results  of  a  series  of  heat  runs  made  on  a 
motor  similar  to  that  shown  in  Fig.  232  and  constructed  as 
follows: 


Internal  dia.  of  stator 

Frame  length 

Peripheral  velocity  of  rotor .  . 

Stator  copper  loss 

Rotor  copper  loss 

Iron  loss 

Total  loss 

External  radiating  surface . .  . 


.  .  .20  in. 

.  .  .5.5  in. 

.  .  .  4730  ft.  per  minute 

.  .  .0.77  kw. 

.  .  .0.9  kw. 

.    .0.77kw. 

.  .  .2.44  kw. 

.  .  .  3260  sq.  in. 


384 


ELECTRICAL  MACHINE  DESIGN 


Opening  in 

housings 

Openings  in 

Openings  in 

closed  with 

housings 

housings 

perforated 

closed  with 

closed  with 

Parts  of  motor 

Open 
motor 

sheet  metal 
f-in.  holes  on 

sheet  metal 

sheet  metal 

f-in.  centers 

Yoke  open- 

Yoke open- 

Yoke open- 

ings open 

ings  open 

ings  closed 

Stator  coils 

18.5 

22 

46 

74 

Stator  iron  

18.5 

20 

48 

71 

Rotor  cond 

15 

21 

46 

71 

Hotor  ring  

14 

21 

44 

69 

Rotor  iron 

14 

20 

41 

61 

Oil  in  bearings  

14 

24 

39 

57 

Outside  of  yoke 

30 

The  temperature  rise  is  given  in  deg.  cent. 

The  first  machine  of  a  new  type  that  is  built  is  generally  very 
liberally  designed,  the  copper  and  iron  densities  are  low.  If  this 
machine  runs  cool  in  test  it  may  get  a  higher  rating  than  that  for 
which  it  was  originally  built,  and,  based  on  the  results  of  the  tests 
on  this  machine,  the  next  is  designed  more  closely.  Electrical 
design  is  not  an  exact  science  but  is  always  changing  to  suit  the 
requirements  of  the  customer,  the  accumulating  experience  of 
the  designer,  and  the  competition  of  other  manufacturers. 


CHAPTER  XXXVI 
NOISE    AND    DEAD    POINTS    IN    INDUCTION   MOTORS 

279.  Noise  due  to  Windage. — Fig.  252  shows  the  standard 
construction  used  for  induction  motors.  As  the  rotor  revolves 
air  currents  are  set  up  in  the  direction  shown  by  the  arrows,  and 
it  may  be  seen  from  diagram  A  that  a  puff  of  air  will  pass  through 
the  stator,  between  the  stator  coils,  every  time  a  rotor  tooth 
comes  opposite  a  stator  tooth,  so  that  the  machine  acts  as  a  siren. 


FIG.  252. — Windage  in  induction  motors. 

The  intensity   of  the  note  emitted  depends  on  the  peripheral 
velocity  of  the  rotor,  while  its  pitch  or  frequency 


=  the  number  of  puffs  per  second 
=  the  number  of  rotor  slots  X  revolutions  per  second 
_  peripheral  vel.  of  rotoran  ft.  per  min. 
5  X  rotor  slot  pitch  in  inches 


(54) 


The  higher  the  pitch  of  the  note  the  more  objectionable  it 
becomes,  and  a  note  with  a  frequency  greater  than  1560  cycles 
per  second,  which  is  the  high  G  of  a  soprano,  is  very  objectionable 
if  loud  and  long  sustained.  For  a  peripheral  velocity  of  8000  ft. 
per  minute  and  a  rotor  slot  pitch  of  1  in.,  the  frequency  of  the 
windage  note  is  1600  cycles  per  second. 

Noise  due  to  windage  can  be  lowered  in  intensity  by  blocking 

up   the  rotor   vent  ducts;  if  the  motor  then  runs  hot  due  to 

poor  ventilation,  some  other  method  of  cooling  must  be  adopted 

such  as  blowing  air  across  the  external  surface  of  the  punchings, 

25  385 


386 


ELECTRICAL  MACHINE  DESIGN 


or  the  motor  may  be  totally  enclosed  and  cooled  by  forced 
ventilation.  The  intensity  of  the  note  can  be  greatly  reduced 
by  staggering  the  vent  ducts  as  shown  in  Fig.  253,  and  since  the 
air-gap  clearance  is  large  in  high-speed  machines,  which  are  the 
only  ones  that  are  noisy  due  to  windage,  the  ventilation  of  such 
machines  will  not  be  seriously  affected.  It  should  also  be  noted 
that  for  high-speed  machines  a  large  number  of  narrow  ducts  will 
give  quieter  operation  than  a  smaller  number  of  wide  ducts, 
because  the  velocity  of  the  air  through  each  duct  will  be  reduced. 
280.  Noise  due  to  Pulsations  of  the  Main  Flux. — In  Fig.  237, 
page  356,  A  shows  part  of  a  machine  which  has  a  large  number  of 
rotor  slots.  The  flux  in  a  rotor  tooth  pulsates  from  a  maximum 
when  the  tooth  is  in  position  x,  to  a  minimum  when  the  tooth 
is  in  position  y,  and  the  frequency  of  this  pulsation  is  equal  to 


I 


FIG.  253. — Motor  with  staggered 
vent  ducts. 


A  B 

FIG.  254. — Variation  of  the  force 

of  magnetic  attraction  on  the  rotor 

tooth  tips. 


the  number  of  stator  teeth  X  revolutions  per  second.  This 
pulsation  of  flux  causes  a  noise  which  varies  in  intensity  with 
the  voltage.  To  minimize  this  noise  the  machine  should  be 
designed  so  as  to  have  a  minimum  pulsation  loss,  the  condition 
for  which,  as  shown  in  Art.  257,  page  356,  is  that  the  rotor  tooth 
shall  be  equal  to  the  stator  slot  pitch,  and  the  rotor  slit  shall  be 
narrow.  The  noise  due  to  pulsation  of  the  main  flux  may  be 
minimized  by  stacking  the  rotor  tightly. 

281.  Noise  due  to  Vibration  of  the  Rotor  Tooth  Tips.— Fig.  254 
shows  several  of  the  slots  of  the  stator  and  rotor  of  an  induction 
motor.  When  the  rotor  tips  are  in  the  position  shown  at  A 
there  is  a  force  of  attraction  between  the  stator  tooth  and  the 
rotor  tooth  tip,  while  in  position  B  this  force  is  zero;  the  rotor 
tooth  tip  will  therefore  be  set  in  vibration  with  a  frequency  equal 


NOISE  AND  DEAD  POINTS  387 

to  the  number  of  stator  teeth  X  revolutions  per  second.  This 
noise  cannot  be  minimized  by  making  the  core  tight  and  must  be 
provided  against  by  having  the  root  y  sufficiently  thick  to  prevent 
bending  and  by  the  use  of  a  moderate  air-gap  clearance.  Noise 
due  to  this  cause  is  rarely  found  in  conservatively  designed 
machines;  it  has  been  found  in  machines  which  are  built  with  a 
small  air-gap  so  as  to  lower  the  magnetizing  current,  and  those 
built  with  a  very  thin  rotor  tooth  tip  so  as  to  lower  the  reactance. 

282.  Noise  due  to  Leakage  Flux. — The  principal  cause  of  noise 
in  induction  motors  is  the  variation  in  the  reluctance  of  the 
zig-zag  leakage  path.  When  the  stator  and  rotor  slots  are  in  the 
relative  position  shown  in  B,  Fig.  254,  the  zig-zag  leakage  flux  is 
a  minimum,  and  when  in  the  relative  position  shown  in  A,  is  a 
maximum/ so  that  there  is  a  pulsation  of  flux  in  the  tooth  tips 
and  two  notes  are  emitted  which  have  frequencies  equal  to  the 
number  of  rotor  slots  X  revolutions  per  second  and  the  number 
of  stator  slots  X  revolutions  per  second  respectively. 

To  ensure  that  the  noise  thus  produced  will  not  be  objection- 
able it  is  necessary  to  make  the  variation  in  the  zig-zag  leakage 
flux  a  minimum,  and  the  most  satisfactory  way  to  do  this  is  to 
make  the  zig-zag  leakage  as  small  as  possible.  This  leakage 
flux  is  directly  proportional  to  the  ampere  cond.  per  slot  and 
inversely  proportional  to  the  air-gap  clearance,  and  it  has  been 
found  from  experience  that  in  order  to  prevent  excessive  noise 
up  to  25  per  cent,  overload  the  ratio 

amp.  cond.  per  slot  at  full-load     ,      .  . 

-4—      — ~-         — — -. — 7—     -  should  not  exceed  14X103  for 
air-gap  clearance  in  inches 

machines  with  open  stator  and  partially  closed  rotor  slots,  or 
12X103  for  machines  with  partially  closed  slots  for  both  stator 
and  rotor. 

It  is  also  found  that,  as  the  frequencies  of  the  two  notes  pro- 
duced by  zig-zag  leakage  approach  one  another  in  value,  the 
noise  becomes  more  and  more  objectionable,  and  that,  for  even 

,  .,          ,.      amp.  cond.  per  slot  at  full-load 
lower  values  of  the  ratio       — -. —  — -. — : — -, —    -  than 

air-gap  clearance  in  inches 

those  given  above,  the  noise  will  be  objectionable  if  the  number 
of  rotor  slots  is  within  20  per  cent,  of  the  number  of  stator  slots. 
The  cause  of  the  noise  in  any  given  case  can  readily  be  deter- 
mined. Run  the  motor  on  normal  voltage  and  no-load  and, 
if  it  is  noisy,  the  trouble  is  due  to  windage,  pulsation  of  the  main 
field,  or  weak  rotor  tooth  tips;  then  open  the  circuit,  and  if  the 


388 


ELECTRICAL  MACHINE  DESIGN 


motor  is  still  noisy  the  trouble  is  due  to  windage.  If  the  motor 
is  quiet  on  no-load  but  noisy  when  loaded  the  trouble  is  due  to 
the  zig-zag  leakage  flux. 

283.  Dead  Points  at  Starting. — It  was  shown  in  Art.  245,  page 
341,  that  the  starting  torque  in  synchronous  horse-power  is 
equal  to  the  rotor  loss  at  starting.  If  the  rotor  is  not  properly 
designed  this  torque  may  not  all  be  available. 


Distance  moved  by  Rotor 

B 
FIG.  255. — Variation  in  the  starting  torque. 


In  the  case  of  a  squirrel-cage  motor  at  standstill,  the  applied 
voltage  is  low  and  the  main  flux  therefore  small,  but  the  starting 
current  is  several  times  full-load  current  and  therefore  the  zig-zag 
leakage  flux  is  large.  This  flux  is  a  maximum  when  the  stator 
and  rotor  slots  have  the  relative  position  shown  in  diagram  A, 
Fig.  254,  and  a  minimum  when  they  have  the  position  shown  in 
B,  so  that  there  is  a  tendency  for  the  rotor  to  lock  in  position  A, 
the  position  of  minimum  reluctance.  If  the  force  tending  to 


NOISE  AND  DEAD  POINTS  389 

rotate  the  rotor  is  less  than  that  tending  to  hold  the  rotor  locked, 
then  the  rotor  will  not  start  up. 

A,  Fig.  255,  shows  several  slots  of  a  machine  which  has  five 
stator  slots  for  every  four  rotor  slots,  so  that  when  the  available 
torque  is  a  minimum  every  fourth  rotor  slot  is  in  the  locked 
position.  Diagram  B  shows  the  result  of  a  test  made  on  this 
machine,  the  torque  being  measured  by  a  brake  for  different 
positions  of  the  rotor  relative  to  the  stator;  it  may  be  seen  that 
there  are  five  positions  of  minimum  torque  in  the  distance  of  a 
rotor  slot  pitch. 

In  order  that  the  variation  in  starting  torque  may  be  a  mini- 
mum it  is  necessary  to  make  the  number  of  locking  points  small. 
If  the  number  of  rotor  slots  is  equal  to  the  number  of  stator  slots 
then,  when  the  starting  torque  is  a  minimum,  each  rotor  slot 
will  be  in  the  locked  position;  if  there  are  four  rotor  to  every 
five  stator  slots  then  the  number  of  locking  points  will  be  one- 
fourth  of  the  total  number  of  rotor  slots;  if  the  number  of 
rotor  and  of  stator  slots  are  prime  to  one  another  then  only  one 
rotor  slot  can  be  in  the  locked  position  at  any  instant  and  the 
best  conditions  for  starting  are  obtained.  It  has  been  found  by 
experience  that  the  starting  torque  for  a  squirrel-cage  motor  will 
be  practically  constant,  if  not  more  than  one-sixth  of  the  total 
number  of  rotor  slots  are  in  the  locked  position  at  any  instant. 

Wound-rotor  motors  have  a  regular  phase  winding  and,  in 
order  that  this  winding  may  be  balanced,  the  number  of  rotor  slots 
as  well  as  the  number  of  stator  slots  must  be  a  multiple  of  the 

,.    stator  slots 
number  of  poles  and  of  the  number  of  phases;  the  ratio  — p— 

stator  slots  per  phase  per  pole       , 

must  therefore  =  -        — ,-—          -~r~  £-T-and,  since  the 

rotor  slots  per  phase  per  pole 

number  of  rotor  slots  per  phase  per  pole  is  often  three  or  four, 
it  might  be  expected  that  such  machines  would  not  have  good 
starting  torque  because  of  dead  points.  This  is  not  the  case 
however  because,  at  .starting,  wound-rotor  motors  have  a  large 
resistance  in  the  rotor  circuit,  and  full-load  torque  tending  to 
cause  rotation  is  obtained  with  full-load  current,  therefore  the 
zig-zag  leakage  at  starting  is  much  smaller  than  in  squirrel-cage 
machines  and  the  force  tending  to  cause  locking  is  small. 

If  a  wound-rotor  motor  be  taken  which  has  not  more  than  30 
per  cent,  of  the  rotor  slots  in  the  locking  position  at  any  instant, 
and  full  voltage  be  applied  to  the  stator  while  the  rotor  circuit  is 


390  ELECTRICAL  MACHINE  DESIGN 

open,  then  the  main  flux  will  have  its  normal  value;  it  will  be 
found  that  the  rotor  can  readily  be  rotated  by  hand,  which  shows 
that  dead  points  are  not,  as  generally  stated,  due  to  variations  in 
the  reluctance  of  the  air-gap  to  the  main  field.  If  now  this  same 
motor  be  short-circuited  at  the  rotor  terminals,  so  that  it  is  equiva- 
lent to  a  squirrel-cage  motor  with  low  rotor  resistance,  it  will 
be  found  impossible  in  most  cases  to  get  the  motor  to  start  up 
even  without  load,  because  of  the  locking  effect  of  the  leakage 
flux.  If  resistance  be  inserted  in  the  rotor  circuit  it  will  be 
found  that,  as  the  rotor  resistance  increases,  the  variation  in  the 
starting  torque  becomes  less  and  less,  and  that  when  this  resist- 
ance is  such  that  full-load  torque  is  developed  with  normal  volt- 
age and  full-load  current,  the  variation  in  starting  torque  due 
to  leakage  flux  is  so  small  that  it  can  be  neglected. 


CHAPTER  XXXVII 
PROCEDURE  IN  DESIGN 

284.  The  Output  Equation. 

#  =  2.22  kZ^flQ-8  volts.     See  page  352. 


=  2.22  kZ(BgrLa}(^—^J^~    IIO'8  volts 

_2.22/clQ-8 

120 
nZI 


volts 

-I  i ,)/  \  —   y  "       v  •    • .  -  -  j.-  -  - 

™77 

and  0  = 


7T.D, 

therefore       nE'/  =  n   (  — y20 j  ZBg7iDaLg   r.p.m.    (  ~rJ^ 

L  \  /  J  \ 

™  7?r 

and 


=  2.35 X  lO~12Bgq   cosd  XyX r.p.m.  X Da2Lg 
taking  k=  0.96 

from  which  Da2L&  =^^-  0  ogvx  p10!".^/^..  (55) 


The  value  of  B^,  the  apparent  average  gap  density,  is  limited 
by  the  permissible  value  of  Bt)  the  maximum  stator  tooth  density, 
since 


where  the  iron  insulation  factor  =^-  =  0.9 

L9 

the  permissible  value  of  Bt  =  85,000  lines  per  square  inch  for 

60  cycles 

=  100,000  lines  per  square  inch  for 
25  cycles 

and  y=2.1  approximately,  being  slightly  larger  for  machines  of 
h 

small  pole-pitch 

therefore,  for  machines  jvith  a  pole-pitch  greater  than  7  in., 

391 


392 


ELECTRICAL  MACHINE  DESIGN 


11 


J9MOJ  % 


PROCEDURE  IN  DESIGN 


393 


#0=23,000  lines  per  square  inch  for  60  cycles,  approximately 
=  27,000  lines  per  square  inch  for  25  cycles,  approximately. 

The  Values  of  cos  0  and  y. — The  values  that  may  be  expected 
from  a  line  of  60-cycle  motors  with  open  stator  slots  and  par- 
tially closed  rotor  slots  are  given  in  Fig.  256,  diagram  A,  and 
corresponding  curves  for  a  line  of  25-cycle  motors  are  given  in 
diagram  B. 

Two  power  factor  curves  a  and  b  are  given  for  the  60-cycle 
machines;  these  correspond  to  the  two  speed  curves  a  and  6. 
The  power  factor  increases  very  slowly  for  speeds  above  a  but 
drops  very  rapidly  for  speeds  below  b. 


GOO 


400 


200 


20 
200 


40  60 

400  600 

Brake  Horsepower 


800 


100 
1000 


FIG.  257. — Curve  to  be  used  in  preliminary  design  for  frequencies  between 

25  and  60  cycles. 

The  power  factor  and  efficiency  can  be  improved  by  the  use  of 
partially  closed  slots  for  both  stator  and  rotor. 

285.  The  Relation  between  Da  and  Lg. — There  is  no  simple 
method  whereby  Da2Lg  can  be  separated  into  its  two  components 
in  such  a  way  as  to  give  the  best  machine,  the  only  satisfactory 
method  is  to  assume  different  sets  of  values,  work  out  the  design 
roughly  for  each  case,  and  pick  out  that  which  will  give  good 
operation  at  a  reasonable  cost. 

To  simplify  this  work  the  following  equations  are  developed. 
I0  =  the  magnetizing  current  per  phase 

(7)  _ 

=  0.87  cond.  per  pole XTL7X<5XCXL2'  page  354' 


.  . 

cond.  per  pole 


XBaXd 


394  ELECTRICAL  MACHINE  DESIGN 

taking  C      =  1.5,  an  average  value  for  machines  with  open  stator 
slots  and  partially  closed  rotor  slots. 

therefore  -j  =ihe  per  cent,  magnetizing  current 

=  cond.  per  pole  X/  xB°Xd 

=  2.05— *X^  (56) 

The  minimum  permissible  air-gap  clearance  is  fixed  by  me- 
chanical considerations  and  should  increase  as  the  diameter, 
frame  length  and  peripheral  velocity  increase;  its  value  should 
not  be  smaller  than  that  given  by  the  following  empirical 
formula: 

d  =  0.005  +0.00035Z>a  +  0.001L0 +0.0037  (57) 

where     $  =  the  air-gap  clearance  in  inches 

Da=the  stator  internal  diameter  in  inches 
L0  =  the  gross  iron  in  the  frame  length  in  inches 
F=the  peripheral  velocity  of  the  rotor  in  1000s  of  feet 
per  minute. 

The  ratio  -j-  is  found  as  follows: 


where        E  =  2.22kZcj)afW-8  volts,  formula  25,  page  190. 

=  2.22kZ(BgrLg)flQ-8  volts 

and        Xeq  =  2nfb2c2pn(Kl  +  K2Lg)  10  ~8  ohms,  formula  47,  page 
369. 

-*  ohms 


P 

,        Id     2.22X0.96  /  BgrL 
therefore  -j-      -^ 


>x-£—  (58) 

q       Ki+K2Lg 

The  Value  of  q.  —  From  formulae  55,  56,  and  58  it  may  be  seen 
that  the  larger  the  value  of  q  the  smaller  the  value  of  Da2Lg,  the 
smaller  the  per  cent,  magnetizing  current,  and  the  smaller  the 
circle  diameter  and  therefore  the  overload  capacity.  Since  the 

,.    amp.  cond.  per  inch      , 

copper  heating  depends  on  the  ratio  —  ^-  —  TJ  —  —  ,  the 

cir.  mils,  per  amp.  ; 

larger  the  value  of  q,  the  greater  the  amount  of  copper  required  to 


PROCEDURE  IN  DESIGN 


395 


keep  the  temperature  rise  within  reasonable  limits  and  therefore 
the  deeper  the  slots  and  the  larger  the  slot  reactance.  Fig.  257 
gives  average  values  of  q  for  25-  and  60-cycle  induction  motors 
and  this  curve  may  be  used  for  a  first  approximation. 

286.  Desirable  Values  for  I0  and  Id.— Fig.  258  shows  the  circle 
diagram  for  a  reasonably  good  induction  motor: 


The  power  factor  at  full-load 
The  starting  torque 
The  maximum  torque 
The  maximum  output 


=  90  per  cent 

=  1.5  times  full-load  torque 
=  2.7  times  full-load  torque 
=  2.2  times  full-load 


To  obtain  such  characteristics  the  magnetizing  current  should 
not  exceed  one-third  of  full-load  current,  nor  should  the  maximum 
current  Id  be  less  than  six  times  full-load  current. 


FIG.  258. — Circle  diagram  for  an  average  induction  motor. 

287.  Example  of  Preliminary  Design. — To  simplify  the  work 
the  necessary  formulae  are  gathered  together  below. 

JMX  10" 


r.p.m.    2.35Bgq  cos 
>05^     - 

Ba.  Ln 


where 


,r 
Ki+K2Lg 

Da  =  the  internal  diameter  of  the  stator  in  inches 
L0  =  the  axial  length  of  the  gross  iron  in  inches 
Bg  is  taken  as  23,000  for  60  cycles 
27,000  for  25  cycles 
q  is  found  from  Fig.  257 


396  ELECTRICAL  MACHINE  DESIGN 

cos  6  and  TJ  are  found  from  Fig.  256 

d  =  0.005  +  0.00035Da  +  O.OOIZ^  +  0.0037 
where         7  =  the  peripheral  velocity  of  the  rotor  in  1000s  of 

feet  per  minute. 
Kl  and  KJLg  are  found  by  the  use  of  the  curves  in  Fig.  244. 

The  work  is  carried  out  in  tabular  form  as  shown  below,  where 
the  figures  are  given  for  a  50  h.  p.,  60-cycle7  900  r.p.m.  motor. 

PRELIMINARY  DESIGN  SHEET 


50  h. 

p.,  squirrel  cage,  60  cycles,  900  r.  p.  m. 

50  =  23,000,    5  =  600,    cos  < 

?=  89  per  cent,  r?=8< 

)  per  cent.,  DazLg  = 

2150 

D. 

Lg 

T 

V 

d 

J 

^  +  K2 

Li  i 

7 

la 

I 

Id 

I 

15 

9.5 

5.9 

3.5 

0.03 

3 

,7  +  14 

.(> 

=  18. 

3 

0.4 

6.7 

17 

7.5 

6.7 

4.0 

0.03 

4. 

0  +  10. 

8 

=  14 

.8 

0.35 

6.5 

19 

6.0 

7.5 

4.5 

0.031 

4. 

3+   8. 

I 

=  12 

.4 

0.32 

6.2 

21 

5.0 

8.2 

4.9 

0.032 

4. 

5+   6. 

1 

=  10. 

9 

0.31 

5.9 

23 

4.0 

9.0 

5.4 

0.033 

4. 

7+  4. 

8 

=   9. 

5 

0.29 

5.4 

So  far  as  operation  is  concerned  the  19-in.  diameter  machine  is 
probably  the  best  all-round  machine.  The  15-in.  machine  has 
the  largest  magnetizing  current  and  therefore  the  lowest  power 
factor  while  the  23-in.  machine  has  the  smallest  circle  diameter 
and  therefore  the  smallest  overload  capacity. 

The  shop  conditions  must  be  known  before  the  costs  of  the 
above  machines  can  be  intelligently  compared.  The  cost  of 
yoke,  spider  and  housings  is  greatest  for  the  23-in.  machine,  and 
the  cost  of  assembling  the  cores  is  greatest  for  the  15-in.  ma- 
chine; the  total  cost  is  probably  least  for  the  19-in.  machine, 
but  will  not  vary  very  much  over  the  range  of  machines  shown. 

288.  Detailed  Design. — The  work  of  completing  the  50  h.  p., 
60-cycle,  900  r.p.m.  design  is  carried  out  in  tabular  form  for  the 
440-volt,  three-phase  rating  as  follows : 

Stator  design 

/•X120 

Poles  =  —  =8 

r.p.m. 

Internal  diameter  of  stator  =  19  in.  from  preliminary  design 

Gross  iron  =  6  in.  from  preliminary  design 

Vent  ducts  =  1  -  0.375  in. 

Net  iron  =  0.9  X  gross  iron  =5.4  in. 

Pole-pitch  =  7.46  in. 

Slots  per  pole  =12,  to  be  suitable  for  two  and  three 

phase 


PROCEDURE  IN  DESIGN  397 

if  chosen  .      =6,  the  machine  would  be  noisy,  see 

Art.  282 
if  chosen  =  18,  the  slots  would  be  very  narrow. 

Slot-pitch  =P°le-Pitch  =0.622  in. 

slots  per  pole 

Slot  width  =0.311  =half  the  slot  pitch  for  a  first 

approximation 

Ampere  conductors  per  inch  =600  from  preliminary  design 

Ampere  conductors  per  slot  =374  =  Ampere    cond.    per  inch  X  slot 

pitch 
Full-load  current  =62   amp.    taking   cos    0  =  0.89    and 

r?=0.89 

amp.  cond.  per  slot 
Conductors  per  slot  =8=     .  ,,  ,  —  ^  — 

full-load  current 

Connection  =Y,    because    the    current    in    each 

conductor  was  taken  equal  to  the 
line  current 

Amp.  cond.  per  inch 

n    ^  .,  —  =1.0  from  Fig.  250 

Cir.  mils  per  amp. 

Circular  mils  per  ampere  =600  required 

Circular  mils  per  conductor  =  600  X  full-load  current 

=  37,200 

Size  of  conductor  =0.029  sq.  in. 

Size  of  slot  and  section  of  conductor  are  worked  out  in  tabular  form  thus: 

0.311  in.  =  assumed  slot  width 

0.064  in.  =  width  of  slot  insulation,  see  page  203 

0.04    in.  =  necessary  clearance 

0.207  in.  =  available  width  for  copper  and  insulation  on  conductors 
Use  copper  strip  0.2  in.  wide  insulated  with  double  cotton  Covering  and 
change  the  slot  width  to  0.32  for  a  second  approximation,  therefore  the  size 
of  conductor  =  0.14  in.  X0.2  in. 

0.14    in.  =  depth  of  each  conductor 

0.015  in.  =  thickness  of  the  cotton  covering 

0.155  in.  =  depth  of  each  conductor  and  its  insulation 

0.465  in.  =  depth  of  three  cond.  and  their  insulation 

0.084  in.  =  depth  of  slot  insulation  on  each  coil,  see  page  203. 

0.549  in.  =  depth  of  insulated  coil 

1.098  in.  =  depth  of  two  insulated  coils 

0.1      in.  =  thickness  of  stick  in  top  of  slot 

1.198  in.  =  necessary  depth  of  slot. 

Before  fixing  the  slot  depth  the  windings  for  all  the  probable  ratings  to 
be  built  on  this  frame  should  be  worked  out  and  the  slot  made  deep  enough 
for  the  worst.  In  this  case  a  suitable  slot  depth  is  1.5  in. 

440 
Voltage  per  phase  ~=  2^'  since  the  connection  is  Y 


per  pole  =1,040,000,  from  formula  25,  page  190 

Minimum  tooth  width  =0.302  in.,  taking  slot  width  =0.32  in. 

Minimum  tooth  area  per  pole  =  minimum  tooth  width  X  slots  per  pole  X 

net  iron 


398  ELECTRICAL  MACHINE  DESIGN 

=  19.6  sq.  in. 

.,      .  flux  per  pole  TT 

Maximum  tooth  density  =  —  :  —  —  r~X~ 

mm.  tooth  area  per  pole     2 

=  83,000  lines  per  square  inch. 

Had  this  density  come  out  too  high  it  would  have  been  necessary  to  have 
increased  the  length  of  the  machine  or  decreased  the  slot  width. 

Maximum  core  density  =65,000  lines  per  square  inch,  assumed 

flux  per  pole 

~2Xcore  depth  X  net  iron 

Core  depth  =  1.48  in.  ;  use  1.5  to  give  an  even  figure  for  the 

stator  external  diameter. 

The  above  data  is  now  filled  in  on  the  design  sheet  shown  on  page  402. 

Rotor  design 

Air-gap  clearance  =0.03  in.  from  preliminary  design 

External  diameter  =18.  94  in. 

Gross  iron  =  6  in. 

Vent  ducts  =1—0.5  in.;  slightly  wider  than  for  stator 

Net  iron  =5.4  in. 

stator  slots  , 
Number  of  slots  —  —  »  --  for   quiet   operation,    Art.  282 

page  387. 

With  this  number  =  80  there  would  be  5  rotor  slots  for  every  6  stator 
slots  and  the  starting  torque  would  not  be  uniform,  see  Art.  283,  page  388; 
use  therefore  79  slots. 

Rotor  current  per  cond.  at  full  load 

-I,,  (Fig.  224)xtotalstator  conductors 
total  rotor  conductors 

where  Iu  is  taken  equal  to  0.85  X  /  for  a  first  approximation,  a  value  which 
must  be  checked  after  the  data  for  the  circle  diagram  has  been  calculated 
and  the  circle  drawn. 


=  385  amperes 

385X79 
Ampere  conductors  per  inch  =  — 

=  510 

Amp.  cond.  per  inch 

—  n  —  =1.0approx.,  the  same  as  for  the  stator 

Cir.  mils  per  amp. 

Circular  mils  per  ampere  =510  desired 

Size  of  conductor  =510X385 

=  195,000  circular  mils 

=  0.15  sq.  in.  approximately. 

Size  of  slot  must  be  chosen  so  that  the  flux  density  at  the  bottom  of  the 
rotor  tooth  shall  not  exceed  120,000  lines  per  square  inch  and  the  work  is 
carried  out  as  follows: 


PROCEDURE  IN  DESIGN  399 

Assumed  copper  section,  0.2  in.  X  0.75  in.  0.3  in.  X0.5  in.  0.4  in.  X0.35  in. 
Slot  section  to  allow  for  insulation 

and  clearance,  0.25  in.  X 0.8  in.  0.35  in.  X 0.55  in.  0.45  in.  X 0.4  in. 

Rotor  diameter  at  bottom  of  slot,  17.14  in.  17.64  in.  17.94  in. 

Minimum  slot  pitch,  0.68  in.  0.70  in.  0.72  in. 

Minimum  rotor  tooth,  0.43  in.  0.35  in.  0.27  in. 

Minimum  tooth  area  per  pole,  23  sq.  in.  18.7  sq.  in.  14.4  sq.  in. 

Flux  per  pole,  1.04X106  1.04X106  1.04X106 
Maximum  tooth  density;  lines    per 

square  inch,  71,000  87,000  114,000 

The  wider  and  shallower  the  slot  the  lower  is  the  rotor  reactance  so  that 
the  last  of  the  three  is  chosen,  namely,  0.45  in.  X  0.4  in. 

The  necessary  data  for  the  circle  .diagram  is  now  calculated. 
The  magnetizing  current  =21  amperes,  from  Art.  259,  page  357. 

The  no-load  loss  =1680  watts  iron  loss 

+  810  watts  bearing  friction,  from  Art.  259. 

The  maximum  stator  current    =415  amperes,  from  Art.  264,  page  364. 
The  circle  is  then  drawn  to  scale  as  in  Fig.  247. 
The  section  of  the  rotor  ring  is  found  as  follows: 
The  maximum  stator  conductor  loss  =  57  kw.  Art.  268,  page  373. 

therefore  in  Fig.  247,  ab  =75  amperes 

The  maximum  rotor  conductor  loss   =39  kw.  Art.  268 
therefore  be  =51  amperes 

The  maximum  starting  torque  de- 

.     ,  =90  syn.  h.  p. 

sired  J 


therefore  Im 


:67  syn.  kw. 
67X1000 


1.73X440 
=  88  amperes 

and  bd  =113  amperes 

For  full-load  torque  at  starting  the  rotor  loss 

=  50  syn.  h.  p. 
=  37  syn.  kw. 

of  which  the  loss  in  the  rings         ^^^M 

=  20  kWi 
The  weight  of  the  end  rings  =1  Ib.  per  kw.  loss,  Art.  272,  page  379 

=  201b. 

The  mean  diameter  of  end  ring  =17.5  in.  approximately 

The  section  of  each  end  ring  =0.57  sq.  in. 

The  resistance  factor  for  the  ring  material  is  found  from  formula  50,  namely, 

C/N  67    \2     2)rkr 
loss  in  two  rings  =0.5  (    ^nL    )    X  -^ 


where  /c2=  the  maximum  rotor  current  =  (4 15  — 21) 

=  2880  amperes 

and  the  corresponding  ring  loss  =  1.73X440Xcd 

=  1.73X440X62 
=47,000  watts 


400 


ELECTRICAL  MACHINE  DESIGN 


therefore  47,000  =  0.5  (^»X  ^ 


from  which 


kr  =  3.8 


Certain  standard  compositions  are  used  for  the  end-ring  mate- 
rial, and  in  this  case  a  composition  which  had  five  times  the  resist- 
ance of  copper  was  used,  and  the  ring  section  increased  to  0.75 
sq.  in.  to  keep  the  loss  the  same. 

The  design  is  now  complete  and  the  data  should  be  gathered 
together  in  convenient  form  on  a  design  sheet  similar  to  that  on 
page  402. 

289.  Design  of  a  Wound -rotor  Machine. — It.  is  desired  to 
design  a  rotor  of  the  wound  type  for  the  50-h.  p.,  440-volt, 
3-phase,  60-cycle,  900-r.p.m.  motor  of  which  the  stator  data  is 
tabulated  on  page  402. 

The  work  is  carried  out  in  a  similar  way  to  that  adopted  for  the 
squirrel-cage  design. 


Air-gap  clearance 

External  diameter 
Gross  iron 
Vent  ducts 
Net  iron 

Number  of  slots 

Conductors  per  slot 

Current  per  conductor  at  full-load 

Terminal  voltage  at  standstill 


=  0.03  in.  the  same  as  for  the  squirrel- 

cage  motor 
=  18.94  in. 
=  6  in. 
=  1-0.5  in. 
=  5.4  in. 

stator  slots  .. 

—  =~2  --  for  quiet  operation 

=  80;  use  72  or  9  slots  per  pole 
=  2,  assumed;  this  number  gives  the 
simplest  winding 


=  210  amperes 

-nox72x2 

JX96X6 


=  110 

The  brushes  and  slip  rings  will  be  cheaper  and  easier  cooled  if 
the  winding  is  made  with  4  conductors  per  slot,  Y-connected; 
then 

=  105  amperes 

=  220 

=  510 

=  1.0,  the  same  as  for  the  stator 

=  510 

=  510X105 

=  53,500  cir.  mils 

=  0.042  sq.  in. 


Current  per  conductor  at  full-load 
Terminal  voltage  at  standstill 
Amp.  cond.  per  inch 
Amp.  cond.  per  inch 

Cir.  mils  per  amp. 
Circular  mils  per  ampere  desired 
Size  of  conductor 


PROCEDURE  IN  DESIGN  401 

Size  of  slot  is  found  in  the  same  way  as  for  the  squirrel-cage  machine 
and  that  chosen  in  this  case 

=  0.42  in.  X  1.0  in. 
Size  of  conductor  =0.12  in.  X  0.35  in.  arranged  2  wide  and 

2  deep. 
The  magnetizing  current  =21  amperes,    the    same    as    for  the 

squirrel-cage  machine 

The  iron  loss  =1,680  watts 

The  bearing  friction  loss  =810  watts 

The  maximum  stator  current  is  worked  out  in  a  similar  way  to 
that  for  the  squirrel-cage  machine,  see  Art.  264,  page  364;  thus 
for  a  wound-rotor  machine  the  reactance  per  phase 


where  T  =  7. 5  in. 

^^  =  4.3  from  Fig.  244 

^  =  0.622  in. 
£  =  0.03  in. 


C1      it1 
2  =  1.16 

=m&-< 


A2  =  0.83 

+  <f>z=  1  [.>     /     1.0'        0.1       2X0.07       0.03\ 
n2p   ~72[       \3X0.42  +  0.42+0.42  +  0.1+~07T/ 


=     [5.1  +  2.8] 
const.     =  1  .  5  X  0.  00  1  07,  from  page  367. 


0.00107X1.5X 


) 


^ 

=  0.415X[0.  72+  (0.088  +  0.11  +  0.032)6] 
=  0.87 


254 
Max.  current  per  phase  =  ^=  =  300  amp.  as  against  415  for  the  squirrel- 

cage  motor. 

290.  Induction  Motor  Design  Sheet.  —  All  dimensions  in  inch 
units. 

26 


402 


ELECTRICAL  MACHINE  DESIGN 


Stator         Squirrel  cage     Wound  rotor 


External  diameter, 
Internal  diameter, 
Frame  length, 
End  ducts, 
Center  ducts, 
Gross  iron, 
Net  iron, 
Slots,  number, 

size, 
Cond.  per  slot,  number, 

size, 
Winding,  type, 

connection, 
Minimum  slot  pitch, 
Minimum  tooth  width, 
Core  depth, 
Pole-pitch, 

Minimum  tooth  area  per  pole, 
Core  area, 

Apparent  gap  area  per  pole, 
Flux  per  pole, 
Maximum  tooth  density, 
Maximum  core  density, 
Ampere  conductors  per  inch, 
Circular  mils  per  ampere, 
Length  of  conductors, 
Maximum  current  per  conductor, 
Maximum  conductor  loss, 
Section  of  each  end  connector, 
Resistance  factor, 
Maximum  ring  loss, 
Apparent  gap  density, 
Air-gap  clearance, 
Carter  coefficient, 
Magnetizing  current,  gap, 
total, 


Reactance  per  phase, 

Maximum  line  current  Id, 

Rating 

Horse-power, 

Terminal  voltage, 

Amperes,  full-load, 

Phases, 

Frequency, 

Syn.  r.p.m., 

Poles, 


25 

18.94 

18.94 

19 

15.5 

14.5 

6.375 

6.5 

6.5 

none 

none 

none 

1-0.375 

1-0.5 

1-0.5 

6 

6 

6 

5.4 

5.4 

5.4 

96 

79 

72 

0.32X1.5 

0.45X0.4 

0.42X1.0 

6 

1 

4 

0.14X0.2 

0.4X0.35 

0.12X0.35 

double-layer 

squirrel-cage 

double-layer 

Y 

Y 

0.622 

0.72 

0.73 

0.302 

0.27 

0.31 

1.5 

1.22 

1.12 

7.46 

19.6 

14.4 

15 

8.1 

6.6 

6.0 

45 

1.04X106 

1.04X106 

1.04X106 

83,000 

114,000 

110,000 

64,000 

79,000 

86,000 

600 

510 

510 

570 

460 

510 

20.5 

10.5 

19 

415 

2,880 

560 

57  kw. 

39  kw. 

32  kw. 

0.75 

5.0 

47  kw. 

23,000 

0.03 

1.52 

1.03 

1.03 

17.6 

21 

12 

16.75  stator 

0.62 

0.87  stator 

415 

2,880 

300  stator 

50 

440 

62 

385 

105 

3 

60 

900 

8 

PROCEDURE  IN  DESIGN 


403 


V 


13 

13 

10.2 

2.55 

15 

9.75 

11.8 

2.95 

17 

7.6 

13.3 

3.34 

19 

6.1 

14.9 

3.74 

21 

5.0 

16.5 

4.12 

K  +KL                 ^ 

Id 

I 

I 

5. 

0  +  14. 

4 

=  19 

.4 

0. 

27 

10 

.2 

5. 

4  +  10. 

0 

=  15 

.4 

0. 

23 

9 

.0 

5, 

,7+   7. 

2 

=  12 

.9 

0. 

19 

9 

.0 

6, 

0+   5. 

4 

=  11 

.4 

0. 

18 

8 

.1 

6. 

4+   4. 

2 

=  10 

.6 

0. 

17 

7 

.2 

291.  Design  of  a  25-cycle  Motor. — It  is  required  to  design  a 
motor  of  the  following  rating: 

50  h.  p.,  440  volts,  3-phase,  25-cycle,  750  r.p.m.,  squirrel  cage. 
£0  =  27,000;  g=600;  cos  0  =  90  per  cent.;  r?=89  per  cent.;  Da2Lg  = 

d 

0.30 
0.29 
0.28 
0.29 
0.30 

Any  one  of  these  machines  would  be  satisfactory  as  far  as 
magnetizing  current  and  overload  capacity  are  concerned.  The 
13-in.  machine,  however,  is  long  and  difficult  to  ventilate  prop- 
erly so  that  it  need  not  be  considered.  Of  the  others,  the 
machine  with  the  smallest  diameter  will  generally  be  the  cheapest 
so  that  the  choice  lies  between  the  15-  and  the  17-in.  machine; 
there  will  be  very  little  difference  in  cost  between  the  two,  but 
the  17-in.  machine  will  be  the  easier  to  ventilate  properly  and 
will  have  the  better  appearance. 

Detailed  Design  for  the  17-in.  Machine. — Since  the  per  cent, 
magnetizing  current  is  small  it  will  be  advisable  to  increase 
the  air-gap  over  the  minimum  value  of  0.029  in.;  it  may  be 
taken  =0.04  in.  without  making  the  magnetizing  current  too 
large  or  the  power  factor  at  full-load  too  low. 


Poles, 

Internal  diameter  of  stator, 

Gross  iron, 

Vent  ducts, 

Net  iron, 

Slots  per  pole, 

slot  pitch 

amp.  cond.  per  slot 

amp,  cond.  per  slot 

air-gap  clearance 


Slots  per  pole, 

Pole-pitch, 

Slot  pitch, 

Slot  width, 

Ampere  conductors  per  inch, 

Amperes  conductors  per  slot, 


=  4 

=  17  in. 
=  7. 5  in. 
=  2-0.5  in. 
=  6. 8  in. 
=  12     or 
=  1.12  in. 
=  670 

=  17X103 
Noisy 


18 

0.74  in. 
445 

11  X103 


Quiet,    see    Art.    282, 

page  387 

=  18,    suitable   for   both   two- and 
three-phase 
=  13. 4  in. 
=0.74  in. 
=  0.37  in. 

=  600  from  preliminary  design 
=  445 


404  ELECTRICAL  MACHINE  DESIGN 

Full-load  current,  =61 

Conductors  per  slot,  =  7 . 3  if  Y-connected 

=  1 2 . 6  if  A  -conne  cted 
Amp.  cpnd.  per  inch, 

— ^r. TJ =  U  .  o  & 

Cir.  mils  per  amp. 
Ampere  conductors  per  inch  for 

12  A  winding.  =570 

Circular  mils  per  ampere,  =  700 

Amperes  per  conductor,  =35  for  a  delta-connected  winding 

Circular  mils  per  conductor,  =25,000 

Section  of  conductors,  =0.02  square  inch. 

=  0.08X0. 25  in. 

Size  of  slot,  =0.37 XI. 75  in. 

Voltage  per  phase,  =440  since  connection  is  A 

Flux  per  pole,  =  2, 900, 000 

Minimum  tooth  width,  =0.37  in. 

Minimum  tooth  area  per  pole,  =45. 5  square  inch. 

Maximum  tooth  density,  =  100,000  lines  per  square  inch. 

The  rotor  of  this  machine  may  be  designed  by  the  same  method 
as  that  adopted  for  the  60-cycle  machine  in  Art.  288;  the  probable 
number  of  slots  =  59. 

It  might  seem  that,  since  the  overload  capacity  is  more  than 
sufficient  for  all  ordinary  purposes,  a  value  of  q  higher  than 
600  might  have  been  used.  This  would  have  allowed  the  use  of  a 
slightly  shorter  machine,  as  may  be  seen  from  formula  55,  page 
391,  but  would  have  necessitated  a  larger  section  of  copper  to 
keep  the  heating  within  reasonable  limits,  and  a  larger  number 
of  conductors  per  slot.  It  is  probable  that  the  small  decrease 
in  length  of  the  machine  would  have  been  more  than  compensated 
for  in  price  by  the  increased  amount  of  copper  required  for  both 
stator  and  rotor. 

292.  Variation  in  the  Length  of  a  Machine  for  a  Given  Diameter. 
— In  order  to  save  on  the  original  outlay  for  the  tools  required 
to  build  a  line  of  induction  motors  it  is  advisable  to  design  at 
least  two  lengths  of  machine  for  each  diameter.  In  the  case  of 
small  factories,  where  the  total  output  is  not  very  large,  three 
different  frame  lengths  may  be  used  for  each  diameter. 

The  principal  dimensions  of  three  squirrel-cage  machines  built 
on  a  19-in.  diameter  for  8  poles,  60  cycles  and  900  r.p.m.  are 
tabulated  below. 

External  diameter  of  stator,       25  in.  25  in.  25  in. 

Internal  diameter  of  stator,         19  in.  19  in.  19  in. 

Frame  length,  4. 5  in.  6.375  in.  8.125  in. 


PROCEDURE  IN  DESIGN  405 


Center  ducts, 

none 

1-0.375  in. 

1-0.375  in. 

Gross  iron, 

4.  5  in. 

6  in. 

7.75  in. 

Net  iron, 

4.05  in. 

5.4  in. 

7.0  in. 

Slots, 

96 

96 

96 

Size  of  slot, 

.32  in.  XI.  5  in 

.  .32  in.  XI.  5  in. 

.32  in.  XI.  5  in. 

Conductor  per  slot, 

8 

6 

8 

Size  of  conductor, 

0.1in.X0.2in. 

0.14in.X0.2in. 

0.1  in.  X  0.2  in. 

Connection, 

Y 

Y 

A 

Ampere  conductors  per  inch, 

580 

600 

600 

Circular  mils  per  ampere, 

560 

580 

600 

Amperes  per  conductor, 

45 

62 

46.5 

Amperes  per  terminal, 

45 

62 

80 

Terminal  voltage, 

440 

440 

440 

Phases, 

3 

3 

3 

Output, 

35  h.  p. 

50  h.  p. 

65  h.  p. 

Air  gap  clearance, 

0.03  in. 

0.03  in. 

0.03  in. 

Magnetizing  current, 

16  amp. 

21  amp. 

27  amp. 

Kl  actual,  see  Fig.  245,  page  369, 

4.30 

4.30 

4.30 

K2Lg  actual, 

5.90 

7.90 

9.90 

Reactance  per  phase  in  ohms, 

0.92 

0.62 

1.27 

Maximum  current  in  line, 

275  amp. 

410  amp. 

600  amp. 

Magnetizing  current, 

35  per  cent. 

34  per  cent. 

34  per  cent. 

Maximum  current, 

6.1  full-load 

6.6  full-load 

7.5  full-load. 

The  above  machines  are  discussed  under  the  following 
heads: 

Conductors  per  Slot. — Since  the  same  stator  punchings  are  used 
in  each  case,  the  number  of  slots  is  fixed,  and  for  the  same  flux 
density  in  the  different  machines  the  flux  per  pole  must  be 
directly  proportional  to  the  net  iron.  Now  the  voltage  per 
conductor  is  proportional  to  the  flux  per  pole,  so  that  the  number 
of  conductors  in  series,  for  the  same  voltage  per  phase,  must  be 
inversely  proportional  to  the  flux  per  pole  and  therefore  inversely 
proportional  to  the  net  iron  in  the  frame  length. 

Size  of  Conductor. — This  is  inversely  proportional  to  the 
number  of  conductors  per  slot  for  the  same  total  copper  section 
per  slot. 

Current  Rating. — For  the  same  current  density  in  the  conduc- 
tors, the  current  in  each  conductor  must  be  proportional  to  the 
conductor  section.  If  the  connection  is  Y,  the  current 
rating  is  the  same  as  the  current  per  conductor;  if  the  con- 
nection is  A,  the  current  rating  =1.73  times  the  current  per 
conductor. 

Output. — For  the  same  total  section  of  copper,  the  output  of 
the  machine  is  proportional  to  the  net  iron  in  the  frame  length, 


406  ELECTRICAL  MACHINE  DESIGN 

because  output  =  a  const.  X  phases  X  volts  per  phase  X  current  per 

phase 

=  a  const.  X  n X  Z(j>a  Xlc 
=  a  const.  XnZIc X <j>a 
=  a  const.  X total  copper  section XLn 

Magnetizing  Current  =  ?r^r  — r  XBgX§XC,  and 

0.87  X  cond.  per  pole 

since  Bg,  d  and  C  are  all  constant,  the  magnetizing  current  is 
inversely  proportional  to  the  number  of  cond.  per  pole  and 
therefore  to  the  number  of  conductors  per  slot. 

Maximum  Current. — The  leakage  flux  per  phase  is  made  up  of 
two  parts,  the  end-connection  leakage  which  is  independent  of 
the  frame  length,  and  the  slot  and  zig-zag  leakages  which  are 
directly  proportional  to  the  frame  length.  The  reactance  per 
phase  =2nfb2c2pn(K1+K2Lg)W~8 

=  a  const.  Xb2(Kl  +  K2Lg) 
for  machines  built  with  the  same  punchings. 

From  the  data  in  the  table  it  may  be  seen  that,  so  far  as 
magnetizing  current  and  overload  capacity  are  concerned,  the 
longest  machine  is  the  best;  but  a  machine  cannot  be  lengthened 
indefinitely  because  a  point  is  finally  reached  at  which  it  becomes 
impossible  to  cool  the  center  of  the  core  properly,  without  con- 
siderable modification  in  the  type  of  construction.  Even 
before  this  point  is  reached  it  will  generally  be  found  economical 
to  increase  the  diameter  rather  than  keep  on  increasing  the 
length  because,  since  the  output  is  proportional  to  Da2Lg,  an 
increase  in  diameter  of  10  per  cent,  is  equivalent  to  an  increase 
in  frame  length  of  22  per  cent. 

293.  Windings  for  Different  Voltages.— The  stator  of  a  35-h.  p., 
440-volt,  3-phase,  45-ampere,  60-cycle,  900-r.p.m.  induction 
motor  is  constructed  as  follows : 

Internal  diameter  of  stator 19  in. 

Frame  length 4 . 5  in. 

Slots,  number 96 

Slots,  size 0 . 32  X  1 . 5  in. 

Conductors  per  slot,  number 8 

size 0.1X0.2 

Connection Y 

It  is  required  to  design  windings  for  the  following  voltages: 
220  volts,  3  phase,  60  cycles 
550  volts,  3  phase,  60  cycles 


PROCEDURE  IN  DESIGN 


407 


250  volts,  3  phase,  60  cycles 
550  volts,  2  phase,  60  cycles. 

Conductors  per  slot. 
E  =  2.22kZfiaflQ-8  volts 

7      cond.  per  slot  ,  ..  ,  , 

=  a  const.  X&X—    — r^          —  for  a  given  frame  and  frequency, 
phases 

For  the  machine  in  question  A;  =  0.956  for  three-phase  windings 

.     =0.908  for  two-phase  windings 

volts  per  phase  X  phases 

and  the  constant  = j-f      ^ —     — f-r 

A;  X  cond.  per  slot 

440 


0.956X8 
=  100 
The  windings  for  the  different  voltages  may  be  tabulated  thus: 


Term, 
voltage 

Phases 

Volts  per 
phase 

Conductors 
per  slot 

Connec- 
tion 

440 

3 

254 

8 

Y 

220 

3 

127 

4 

Y 

Use  8  conductors  per  slot  con- 

nected YY. 

550 

3 

320 

10 

Y 

250 

3 

144 

4.55 

Y 

An  impossible  winding. 

250 

8 

A 

Use  instead  of  the  one  above. 

550 

2 

550 

12.2 

Single 

Use  12  conductors  per  slot. 

circuit 

Size  of  Conductor. — This  must  be  chosen  so  that  the  stator 
copper  loss  and  copper  heating  are  the  same  for  each  voltage; 
that  this  may  be  the  case  it  is  necessary  to  keep  the  ratio 

amp.  cond.  per  inch  .  .    , 

— r^ — TJ —  -  constant.     The    work    is    carried    out    in 

cir.  mils  per  amp. 

tabular  form  thus: 


-j 

I* 

0 
a    . 

S3 

§ 

i* 

J2   d 

| 

ll 

1 

+3  .s 

«  S 

—  •  "o 

1 

o    o 

S  a 

'§  S 

o 

A 

0}         *H 

0)     O 

rt  ^ 

a 

• 

. 

T3 

H   ° 

CM 

3    -2 

3 

6  p, 

O    ft 

I 

0 

0 

0 

^ 

O 

440 

3 

45 

45 

8 

Y 

580 

560 

0.1X0.2  in. 

220 

3 

90 

45 

8 

YY 

580 

560 

0.1X0.2  in. 

550 

3 

36 

36 

10 

Y 

580 

560 

0.08X0.2  in. 

250 

3 

80 

46 

8 

A 

600 

600 

0.11X0.  2  in. 

550 

2 

31 

31 

12 

1  circuit 

600 

610 

0.075X0.2  in. 

408  ELECTRICAL  MACHINE  DESIGN 

The  rotor  winding  is  the  same  for  all  stator  voltages  and 
phases,  because  the  only  connection  between  the  stator  and  rotor 
is  the  flux  in  the  air-gap,  and  this  is  kept  constant  by  the  use  of 
the  proper  number  of  stator  conductors  per  slot.  It  is  therefore 
possible  to  build  motors  for  stock,  complete  except  for  the  stator 
winding,  which  winding  can  be  specified  when  the  voltage  and 
number  of  phases  on  which  the  machine  will  operate  are  known. 

It  must  not  be  imagined  that  the  designs  which  have  been 
worked  out  in  this  chapter  are  the  only  ones  that  could  have 
been  used.  Electrical  design  is  very  flexible  and  different  values 
for  flux  density  and  ampere  conductors  per  inch  might  have  been 
used  to  give  a  satisfactory  machine,  and  perhaps  a  cheaper  one. 
Where  labor  is  cheap  it  will  often  pay  to  use  closed  stator  slots, 
fans,  forced  ventilation  or  other  means  to  reduce  the  size  of  the 
machine  for  a  given  output. 

When  one  design  for  a  given  rating  is  worked  out  completely, 
the  designer  has  to  go  over  it  and  try  the  effect  of  changing  the 
different  quantities  until  he  is  satisfied  that,  for  the  shop  in 
which  machines  of  his  design  will  be  built,  the  final  design  will 
give  the  most  satisfactory  machine  both  as  regards  manufacturing 
cost  and  reliability  when  in  service. 


CHAPTER  XXXVIII 

SPECIAL   PROBLEMS  IN   INDUCTION  MOTOR   DESIGN 
294.  Slow  Speed  Motors. 
Since  y  =  2.05^  formula  56,  page  394 

and  ^  =  0.337      J3^  T  -r  formula  58,  page  394 

-- 


therefore  ~  =  a  const.  &fv,  *—?  (59) 


and  the  ratio  T  depends  largely  on  the  ratio  -«-• 
1  0  o 

'.        la       6  full-load  current 

In  moderate  speed  machines  7-=rr>,rr^~rfi      •,  —          —=18. 

I0    0.33  full-load  current 

In  high  speed  machines  the  dimensions  are  small  and  the  pe- 
ripheral velocity  high,  so  that  the  ratio  -^  is  generally  large,  since 

the  value  of  r  is  directly  proportional  to  the  peripheral  velocity 
and  the  value  of  d  increases  with  the  dimensions  of  the  machine. 
Such  machines  therefore  have  a  large  value  of  Id  and  a  large 
overload  capacity,  they  have  also  a  small  value  of  I0  and  a 
high  power  factor. 

In  the  case  of  slow  speed  machines  the  dimensions  are  large  so 
as  to  get  the  necessary  radiating  surface,  and  the  peripheral 
velocity  is  generally  low  because  of  the  large  number  of  poles. 

Because  of  the  small  pole-pitch  the  ratio  -^  is  small,  and  the 

LO 

characteristics  of  the  machine  are  small  overload  capacity,  large 
magnetizing  current  and  low  power  factor. 

Compare  for  example  the  preliminary  designs  for  machines  of 
300-h.  p.  output,  60  cycles  and  720  and  300  r.p.m.  respectively. 

Horse-power,  300  300 

Frequency,  60  60 

r.p.m.,  720  300 

409 


410  ELECTRICAL  MACHINE  DESIGN 

Bg,  23,000  23,000 

q,  730  730 

cos  6,  assumed,  91  per  cent.  84  per  cent. 

•t)  assumed  91  per  cent.  90  per  cent. 

DazLg,  12,700  33,500 

Da,  36  in.  65  in. 

Lg,  10  in.  8  in. 

r,  11. 3  in.  8. 5  in. 

V,  in  1000s  of  ft.  per  min.,  6.8  5.1 

d,  0.048  in.  0.051  in. 

Kv  5.3  4.5 

K2Lg,  10.5  10 

,  15.8  14.5 


0.275  0.39 

6.7  5.9 


These  two  machines  are  shown  to  scale  in  Fig.  259. 

The  above  figures  show  that,  the  higher  the  speed  for  a  given 
horse-power,  the  smaller  is  the  magnetizing  current  and  the 
larger  the  overload  capacity;  this  is  a  characteristic  property 
which  cannot  be  changed  except  by  the  use  of  air-gaps  on  the 
slow  speed  machines  which  are  not  large  enough  for  mechanical 
purposes. 

For  slow  speed  motors  the  use  of  25  cycles  offers  considerable 
advantage  over  the  use  of  60  cycles  because,  for  the  same  r.p.m., 
the  number  of  poles  is  the  smaller  in  the  case  of  the  25-cycle 

motor  and  therefore  the  pole-pitch  and  the  ratio  ^  are  the  larger. 

LO 

Compare  for  example  the  preliminary  designs  for  machines  of  300 
h.  p.  at  300  r.p.m.,  for  25-  and  60-cycle  operation  respectively. 

Horse-power,  300  300 

Frequency,  60  25 

r.p.m.,  300  300 

Poles,  24  10 

Bg,  23,000  27,000 

q,  730  730 

cos  6,  assumed,  84  per  cent.  90  per  cent. 

r),  assumed,  90  per  cent.  90  per  cent 

D<?Lg,  33,500  26,500 

Da,  65  in.  46  in. 

Lg,  Sin.  12. 5  in. 

T,  8. 5  in.  14.5    in. 

V,  in  1000s  of  ft.  per  min.,  5.1  3.6 


SPECIAL  PROBLEMS  411 

d,  0.051  in.  0.045  in. 

KV  4.5  5.9 

K2Lg,  10  11.3 

K^  +  KJ.g  14.5  17.2 

0.39  0.235 


7 

^  5.9  9.0 

When  most  of  the  motors  that  are  to  be  used  are  slow  speed 
machines,  that  is,  they  lie  below  the  speed  curve  b  in  Fig.  256, 
then  25-cycle  apparatus  will  have  a  comparatively  high  power 
factor  and  overload  capacity,  while  for  60-cycle  apparatus  these 
will  be  low. 

295.  Closed -slot  Machines. — By  the  use  of  closed  slots  for  both 
stator  and  rotor  the  characteristics  of  slow-speed  machines  can 
be  considerably  improved.  The  only  objection  to  the  use  of 
closed  slots  for  the  stator  is  that  the  windings  are  difficult  to 
repair  in  case  of  breakdown.  There  is  not  the  same  objection  to 
their  use  for  the  rotor  because,  in  the  case  of  the  squirrel-cage 
machine,  there  is  only  one  conductor  per  slot  and  this  is  put  in 
from  the  end,  while  in  the  case  of  the  wound-rotor  machine  the 
winding  can  be  chosen  with  two  or  four  conductors  per  slot 
which  can  be  formed  to  shape  at  one  end,  the  slot  part  and  one 
end  insulated,  and  the  other  end  bent  to  shape. and  insulated  after 
the  conductor  has  been  pushed  into  place.  There  is  no  con- 
nection between  the  stator  applied  voltage  and  the  rotor  voltage 
at  standstill;  this  latter  voltage  can  be  kept  low  by  the  use  of  a 
small  number  of  rotor  conductors  per  slot.  When  the  machine 
is  up  to  speed  and  the  rotor  short-circuited,  the  voltage  between 
the  rotor  windings  and  the  core  is  very  low  and  the  chance  of 
breakdown  small. 

By  the  use  of  closed  slots  the  air-gap  area  is  increased,  and  the 
magnetizing  current  decreased  for  .the  same  winding,  the  slot 
leakage  and  zig-zag  leakage  are  increased  and  the  overload 
capacity  reduced;  as  a  rule  the  increase  in  leakage  is  not  as  large 
as  the  decrease  in  magnetizing  current. 

The  following  table  shows  comparative  designs  for  a  300-h.  p., 
440-volt,  3-phase,  60-cycle,  300-r.p.m.  motor;  the  one  design 
has  open  stator  slots  and  the  other  closed  stator  slots;  the 
rotor  is  of  the  squirrel-cage  type  in  each  case  and  has  closed  slots. 
The  designs  need  not  be  worked  through  carefully,  but  it  is 
necessary  to  understand  the  conclusions  tabulated  at  the  end  of 
the  design  sheet. 


412 


ELECTRICAL  MACHINE  DESIGN 


Inch  units  are  used. 

Open  slot         Closed  slot 
stator                 stator 

Rotor 

Rotor 

External  diameter, 

72 

63 

64.9 

56.9 

Internal  diameter, 

65 

57 

61 

53 

Frame  length, 

9.5 

11 

9.5 

11 

End  ducts, 

2-0.5 

2-0.5 

none 

none 

Center  ducts, 

2-0.5 

2-0.5 

2-0.5 

2-0.5 

Gross  iron, 

8.5 

10 

8.5 

10 

Net  iron, 

7.6 

9 

7.6 

9 

Slots,  number, 

288 

288 

220 

220 

size, 

0.35X1.5 

0.31X1.6 

0.55X0.45 

0.45X0.45 

Conductors  per  slot,  number, 

2 

2 

1 

1 

size, 

0.23X0.5 

0.2X0.5 

0.5X0.4 

0.4X0.4 

Winding,  type, 

double  layer 

double  layer 

squirrel  cage 

squirrel  cage 

connection, 

A 

YY 

Minimum  slot  pitch, 

0.71 

0.62 

0.91 

0.8 

Minimum  tooth  width, 

0.36 

0.31 

0.36 

0.35 

Core  depth, 

2 

1.4 

1.4 

1.4 

Pole-pitch, 

8.5 

7.45 

Minimum  tooth  area  per  pole, 

33 

33.5 

25 

29 

Core  area, 

15.2 

12.6 

10.6 

12.6 

Apparent  gap  area  per  pole, 

72.5 

74.5 

Flux  per  pole, 

1.8X106 

2.08X106 

1.8X106 

2.08X106 

Maximum  tooth  density, 

85,000 

97,000 

113,000 

113,000 

Maximum  core  density, 

59,000 

82,000 

85,000 

83,000 

Ampere  conductors  per  inch 

660 

640 

520 

510 

Circular  mils  per  ampere, 

630 

640 

520 

490 

Apparent  gap  density, 

25,000 

28,000 

Air-gap  clearance, 

0.05 

0.05 

Carter  coefficient, 

1.4 

1.04 

1.02 

1.02 

Magnetizing  current,  gap, 

145,  terminal 

140,  terminal 

total; 

175 

168 

KI, 

4.5 

4.2 

K2Lg, 

10.2 

16.4 

Maximum  line  current,  Id, 

3,000 

2,800 

Horse-power, 

300 

300 

Terminal  voltage, 

440 

440 

Amperes,  full-load, 

400 

400 

485 

415 

Phases, 

3 

3 

Frequency, 

60 

60 

Syn.  r.p.m., 

300 

300 

Poles, 

24 

24 

Reactance  per  phase     = 

O-«./*1^2x>2/v\2^i  1    '  ^ 

^e  .    /<f>*  +  <j>e 

,    <f>*  +  <J>Z\T 

,]io- 

Zxjb  c  p  n\j}n 

iP        \    KlP 

i                  I  *^i 

n2p   / 

where  for  machine  A 


2% 


0/1.3      [   0.2  \ 


0 


n2p 


0-05 


1    r       /   0.45         2X0.07       0.03 
\3X0.55    0.55+0.07    0.07 
5.25 
:220 


7.56 

288 


SPECIAL  PROBLEMS 

Reactance  per  phase     =  2;:  X  60  X  22  X  42  X  242  X  3 \~  +  ( ^^ 

\_  Z±       \  zoo 


413 


=  0.256 
Voltage  per  phase         =  440  for  A  connection 

Max.  current  per  phase  = 

=  1720  amp. 

Max.  line  current  =  1 720  X  1 . 73 

=  3000  amp. 

For  machine  B 
<f>eLe    _  .  2 
2n 


n2p 


'288 
10.5 

:288 


7.0 

220 


1.5          2X0.07      0.03 


3X0.31     0.31  +0.1  .      O.I 


OJ62/J_       1          \ 
0.05  \1-04     1.02       / 


°'45     I     2X°-07     l0'03^    IQ260'81/   1 
3X0.45  "r0.45  +  0.07     0.07/  n          0.05  \1.  04 


Reactance  per  phase     =2?rX60Xl2X42X242x3 


=  0.09 

440 
Voltage  per  phase          =     ^_  =254  for  a  Y-connection 

l.Yo 

Max.  current  per  phase  =  Q  QQ 

=  2800 

=  maximum  line  current. 

The  points  of  importance  in  the  above  designs  are: 


Open  slot 
Flux  density,  stator  teeth  ............  85,000 

Flux  density,  stator  core  .............  59,000 

Core  depth  .........................  2  .  0  in. 

Carter  coefficient  ...................  1.4 

Conductors  per  slot  .................  2A  =1.16Y 

Internal  diameter  of  stator  ...........  65  in. 

Flux  per  pole  .......................  1.8X106 

Magnetizing  current  .................  175  amp. 


Maximum  current  .................  .  3,000 


Closed  slot 
97,000 
82,000 
1  .  4  in. 
1  .  04 

2YY  =  1Y 
57  in. 
2.08X106 
168  amp. 
16.4 
2,800 


When  closed  slots  are  used  the  flux  density  may  be  high,  since 
the  pulsation  loss  is  almost  entirely  eliminated. 

The  value  of  the  Carter  fringing  coefficient  is  decreased  and 


414 


ELECTRICAL  MACHINE  DESIGN 


therefore  the  magnetizing  current  is  reduced  for  the  same 
winding  or,  as  in  the  above  machines,  the  number  of  conductors 
is  reduced  for  the  same  magnetizing  current. 

Because  of  the  reduction  in  the  number  of  conductors  the 
stator  internal  diameter  is  decreased  for  the  same  value  of  q,  the 
ampere  conductors  per  inch. 

Because  of  the  reduced  number  of  conductors  the  reactance 
of  the  winding  is  decreased,  and  because  of  the  increase  in  the 
slot  and  the  zig-zag  leakage,  due  to  the  closing  of  the  slot,  the 
reactance  is  increased. 

The  final  result  is  that  the  closed  slot  machine  is  smaller  and 
cheaper  than  the  open  slot  machine,  especially  if,  as  in  Europe, 
the  cost  of  winding  labor  is  cheap;  it  has  the  same  characteristics 
as  the  open  slot  machine. 

If  the  closed  slot  machine  were  made  on  the  same  diameter  as 
the  open  slot  machine  it  would  have  the  better  characteristics. 

296.  High-speed  Motors. — The  number  of  speeds  in  the  useful 
range  for  small  belted  motors  is  smaller  for  25  than  for  60  cycles, 
as  may  be  seen  from  the  following  table: 


Revolutions  per  minute 

.roles 

60  cycles 

25  cycles 

2 

3,600 

1,500 

4 

1,800 

750 

6 

1,200 

500 

8 

900 

375 

10 

720 

300 

for  that  reason,  and  also  because  they  are  cheaper  than  25-cycle 
motors  of  the  same  speed,  60-cycle  motors  should  be  used  where 
most  of  the  driven  machines  are  moderate  speed  belted  machines. 
Compare  for  example  the  preliminary  design  for  a  300  h.  p., 
60  cycle,  720  r.p.m.,  machine  with  that  for  a  300  h.  p.,  25  cycle. 
750  r.p.m.  machine. 


Horse-power, 
Frequency, 
R.p.m., 
Poles 


300 
60 
720 
10 


300 
25 
750 
4 


SPECIAL  PROBLEMS 


415 


cos  6,  assumed, 
T),  assumed, 
D*aLg, 

Da 

Lff, 

V,  in  1000s  of  ft.  per  min. 
9, 

K^Lg, 


Io 

I' 
Id 


23,000 

730 

91  per  cent. 

91  per  cent. 

12,700 

36  in. 

10  in. 

11. 3  in. 

6.8 

0.048  in. 

5.3 
10.5 
15.8 

0.275 
6.7 


27,000 

730 

92  per  cent. 

91  per  cent. 

10,300 

27  in. 

Min. 

2JL  in. 

5.3 

0.045  in. 

7 

10.2 
17.2 

0.16 
10.2 


These  two  machines  are  shown  to  scale  in  Fig.  259. 

Since  the  magnetizing  current  of  the  25-cycle  machine  is  so 
small,  it  will  be  advisable  to  increase  the  air-gap  clearance  and 
thereby  have  less  chance  of  mechanical  trouble. 

Because  the  25-cycle  machine  has  the  smaller  diameter  it 
must  not  be  imagined  that  it  is  the  cheaper  machine.  It  has 
the  smaller  number  of  poles,  the  larger  flux  per  pole  and,  there- 
fore, the  deeper  core.  Due  to  the  large  pole-pitch  the  end  con- 
nections are  long,  and  due  to  the  lower  peripheral  velocity  and 
the  greater  difficulty  in  cooling  the  long  machine,  a  large  section 
of  copper  and  deep  slots  are  necessary.  These  facts  are  shown 
by  the  following  table : 

Horse-power,  300  300 

R.p.m.,  720  750 

Poles,  10  4 

Pole-pitch,  11. 3  in.  21  in. 

Gross  iron,  10  in.  14  in. 

Flux  per  pole  =BgrLg,  2.6X106  8.0X106 

Stator  core  density,  assumed,  65,000  85,000 

Necessary  core  area,  20  sq.  in.  47  sq.  in. 

Core  depth,  2 . 25  in.  3 . 75  in. 

Rotor  core  density,  assumed,  85,000  85,000 

Necessary  core  area,  15  sq.  in.  47  sq.  in. 

Core  depth,  1 . 7  in.  3 . 75  in. 

Length  of  stator  conductor  30  in.  48  in.  from  Fig.  84. 

A  section  through  the  two  machines  is  shown  to  scale  in  Fig. 
259,  from  which  it  may  be  seen  that  the  25-cycle  motor  has  the 


416  ELECTRICAL  MACHINE  DESIGN 

larger  amount  of  material  in  it,  and  will  probably  be  the  more 
expensive  machine. 

In  the  case  of  large  high-speed  motors,  such  as  those  for  direct 
connection  to  centrifugal  pumps  or  for  motor  generator  sets,  care 
must  be  taken  in  the  design  to  ensure  that  the  machines  will  be 
quiet  in  operation. 

Consider  for  example,  the  design  of  a  direct-connected  wound- 
rotor  motor  of  the  following  rating: 

1000  h.  p.,  60  cycles,  900  r.p.m. 
5g  =  24,000,  2=800,  cos  0  =  92  per  cent.,   i?  =  92  per  cent.,  Da2£ff  =  29,000 


Da 

L 

g 

T 

V 

d 

Kl-{-K2Lg 

Io 

I 

Id 

I 

32 

28. 

5 

12.6 

7. 

55 

0.067 

7.5  +  36 

=  43 

.5 

0.33 

6.6 

36 

22. 

5 

14.1 

8. 

45 

0.065 

7.7  +  27 

=  34 

.7 

0.28 

6.6 

40 

18, 

0 

15.7 

9. 

40 

0.065 

8.3  +  20. 

5  =  28, 

.8 

0.26 

6.3 

44 

15. 

0 

17.2 

10. 

3 

0.066 

8.6  +  17 

=  25 

,6 

0.24 

6.0 

When  using  the  curves  in  Fig.  244  to  determine  K1  and  K2  it 
should  be  noted  that,  for  wound-rotor  machines,  the  values  of  Kl 
found  from  the  curve  must  be  multiplied  by  4/3,  and  the  values 
of  K2  must  be  taken  from  the  upper  curve. 

In  order  that  the  noise  of  the  machine  be  not  objectionable 
at  no-load,  the  peripheral  velocity  should,  if  possible,  be  less 
than  8000  ft.  per  min.  and  the  pitch  of  the  windage  note  should 
be  kept  below  1400  cycles  per  second.  The  number  of  rotor  slots 
per  pole  to  satisfy  this  latter  condition  may  be  found  from 
formula  54,  page  385,  namely: 

frequency  of  windage  note  =  rotor  slots  X  revolutions  per  second 

=  1440  if  12  slots  per  pole  are  used. 

For  quiet  operation  at  full-load,  the  number  of  slots  per  pole 
for  the  stator  should  exceed  that  for  the  rotor  by  about  20  per 
cent.;  see  Art.  282,  page  387. 

For  machines  with  15  slots  per  pole,  the  values  of  the  stator 

slot  pitch  =  Q — ~,  of  the  ampere  conductors  per  slot  =  q  X  h,  and 
o  X  1& 

.    amp.  cond.  per  slot  ,  .  ,    ,,          .        ,  .  n  ,      , 

of  the  ratio  — ^-  -  on  which  the  noise  at  full-load 

air-gap  clearance 

largely  depends,  are  given  in  the  following  table: 


SPECIAL  PROBLEMS 


417 


The  last  of  these  machines  is  close  to  the  noise  limit,  and  the 
first  is  too  long  to  ventilate  properly,  so  that  the  choice  lies 


Amp.  cond. 

^ 

amp.  cond.  per  slot 

per  slot 

d 

32 

0.84 

670 

0.067 

10.0 

36 

0.94 

750 

0.065 

11.5 

40 

1.05 

840 

0.065 

12.8 

44 

1.15 

920 

0.066 

13.8 

between  a  machine  of  36-in.  and  one  of  40-in.  diameter.  If  the 
designer  has  been  troubled  with  noisy  machines  he  will  probably 
choose  that  with  the  smaller  diameter,  because  it  will  have  the 
lower  peripheral  velocity,  and,  therefore,  the  lower  intensity  of 
windage  note.  If  he  is  satisfied,  from  experience  with  other 
high-speed  machines  which  have  been  built  and  tested,  that  the 
40-in.  motor  will  not  be  noisy,  then  it  will  probably  be  chosen 
because  it  is  shorter  and  easier  to  ventilate. 

The  rating  of  1000  h.  p.  is  about  the  highest  that  can  safely 
be  built  at  900  r.p.m.  with  the  open  type  of  construction,  since  a 
machine  of  larger  diameter  is  liable  to  give  trouble  due  to  noise, 
and  a  longer  machine  is  liable  to  get  hot  at  the  centre  of  the  core. 
A  larger  diameter  and  a  higher  peripheral  velocity  may  be  used  if 
the  motor  is  partially  enclosed,  so  as  to  muffle  the  noise,  and  then 
cooled  by  forced  ventilation. 

297.  Two-pole  Motors. — Since,  for  induction  motors  operating 
on  25  cycles,  there  is  no  available  speed  between  1500  and  750 
r.p.m.,  the  former  speed  is  largely  used  for  motors  that  are  direct- 
connected  to  centrifugal  pumps,  and  would  also  be  largely  used 
for  small  belted  motors  were  it  not  that  the  cost  of  a  1500-r.p.m. 
motor  is  seldom  less  than  that  of  a  750-r.p.m.  machine  of  the  same 
horse-power. 

Consider  for  example,  comparative  designs  for  a  300-h.  p. 
25-cycle  induction  motor  at  1500  and  at  750  r.p.m.  respectively. 


Horse-power, 

R.p.m., 

Poles, 


cos  d,  assumed, 
27 


300 

750 

4 

27,000 

730 

92 


300 

1,500 

2 

27,000 

730 

93 


418 


ELECTRICAL  MACHINE  DESIGN 


i),  assumed, 

Da*Lg, 

Da> 


g, 


, 

V,  in  1000s  of  ft.  per  min. 
d 

Klt 
K2Lg, 


Flux  per  pole, 

Core  density;  lines  per  sq.  in. 

Core  area, 

Core  depth, 

Length  of  stator  conductor, 


91 

10,300 
27  in. 
14  in. 
21  in. 
5.3 

0.045  in. 
7 

10.2 
17.2 

0.16 

10.2 

8.0X106 
85,000 

47  sq.  in. 
3. 75  in. 

48  in. 


90 

5,100 

18  in. 

16  in. 

28  in. 

7.0 

0.048  in. 

8 

9.3 

17.3 

0.13 

11.5 

12.0X106 
85,000 
71  sq.  in. 
5  in. 
62  in. 


Some  idea  as  to  the  relative  proportions  of  these  two  machines 
may  be  obtained  from  Fig.  259. 

When  full-pitch  windings  are  used  for  induction-motor  stators, 
the  revolving  field  consists  of  a  fundamental  and  harmonics.  If 
there  is  a  pronounced  nth  harmonic,  the  resultant  revolving 
field  may  be  considered  as  the  resultant  of  a  fundamental 
which  revolves  at  synchronous  speed,  and  of  a  harmonic  which 
revolves  at  n  times  synchronous  speed;  if  these  fields  move  in  the 
same  direction  the  resultant  torque  curve  will  be  curve  3,  Fig. 
260,  which  is  made  up  of  curves  1  and  2,  due  to  the  fundamental 
and  the  harmonic  respectively.  One  of  the  characteristics  of 
the  two-pole  motor,  and  particularly  of  the  two-pole  25-cycle 
motor,  is  its  large  pole-pitch  and  consequent  large  overload 
capacity,  so  that  for  such  machines,  when  of  the  squirrel-cage 
type  and  designed  with  small  slip  in  order  to  obtain  high  efficiency, 
the  overload  torque  ab  of  the  harmonic  may  become  compar- 
able with  the  normal  torque  of  the  fundamental,  and  in  such  a 
case  the  motor  will  run  at  a  speed  ra,  which  is  approximately 

-th  of  synchronous  speed,  and  is  called  a  sub-synchronous  speed. 

IV 

This  sub-synchronous  locking  speed  may  be  eliminated  by  the 
use  of  a  high-resistance  rotor,  which  raises  the  part  cd  of  curve  1 
without  affecting  the  overload  torque;  an  extreme  case  of  a 
high-resistance  rotor  is  a  rotor  of  the  wound  type.  Another  way 
to  eliminate  these  locking  speeds  is  to  eliminate  the  harmonics 


SPECIAL  PROBLEMS 


419 


by  the  use  of  a  short-pitch  winding  in  the  stator.  Fig.  261 
shows  the  flux  distribution  curve  for  a  machine  with  a  large 
number  of  stator  slots;  in  diagram  A  a  full-pitch  winding  is  used, 
while  in  diagram  B  the  winding  is  made  2-/3  of  full-pitch;  it  may 
be  seen  that  in  the  latter  case  a  nearer  approach  to  a  sine  wave  is 


300  H.  P.  720  R.  P.  M.  60  Cycle 


300  H.  P.  300  R.  P.  M.  60  Cycle 


300  H.  P.  750  R.  P.  M.  25  Cycle  300  H.  P.  1500  R.  P.  M.  25  Cycle 

FIG.  259. — 300  h.p.  induction  motors  for  different  speeds  and  frequencies. 

obtained  than  in  the  former.  The  short-pitch  winding  has  the 
additional  advantage  that  it  reduces  the  length  of  end  connec- 
tions considerably  and  for  that  reason  is  useful  for  both  two-  and 
four-pole  machines.  Against  this  advantage  there  is  the  dis- 
advantage that,  since 

E  =  2.22kZ<t>nflQ-*  cos- 

2i 

where  6  is  the  angle  in  electrical  degrees  by  which  the  pitch  is 


420 


ELECTRICAL  MACHINE  DESIGN 


shortened,  therefore,  for  the  same  flux  per  pole,  a  larger  number 
of  conductors  is  required  with  a  short  than  with  a  full  pitch 
winding.1 


\\7 

T* 

FIG.  260. — Speed  torque  curve  for  a  motor  with  harmonics  in  the  wave  of 

flux  distribution. 


298.  Effect  of  Variations  in  Voltage  and  Frequency  on  the 
Operation. — For  a  given  machine 
E  =  &  const. 
70  =  a  const. 
Xeq  =  a,  const.  X/ 

Tjl 

Id  =  Y^~  =  a  const.  X(j> 


X 


cq 


If  the  voltage  applied  to  the  motor  terminals  is  reduced,  the 
value  of  <J)a,  the  flux  per  pole,  will  be  reduced,  and  therefore, 
70  will  be  reduced  and  the  power  factor  improved; 
Id  will  be  reduced  and  the  overload  capacity  decreased. 
The  flux  density  will  be  reduced,  the  current  will  be  increased 
for  the  same  output,  and  the  result  will  probably  be  increased 
heating  and  a  liability  to  pull  out  of  step. 

If  the  voltage  be  increased,  the  value  of  the  flux  per  pole  will 
be  increased  and  therefore, 

1  For  a  discussion  of  short-pitch  windings  see  Adams,  Transactions  of 
A.  I.  E.  E.,  Vol.  26,  page  1485. 


SPECIAL  PROBLEMS 


421 


I0  will  be  increased  and  the  power  factor  decreased; 
Id  will  be  increased  and  so  also  will  be  the  overload  capacity; 
The  flux  density  will  be  increased,  but  the  current  will  be  reduced 
for  the  same  rating,  and  the  result  will  be  reduced  heating. 

If  the  frequency  of  the  applied  voltage  be  reduced,  the  voltage 
being  unchanged,  then  the  flux  per  pole  will  be  increased  and  so 
also  will  be  the  magnetizing  current  and  the  overload  capacity. 


Short  pitch  winding 

FIG.  261. — Flux  distribution  in  the  air  gap. 

The  core  loss  and  copper  loss  will  be  practically  unchanged,  but 
the  heating  will  be  increased  due  to  the  reduction  in  speed. 

If  the  frequency  be  increased,  the  voltage  being  unchanged, 
then  the  flux  per  pole  will  be  reduced  and  so  also  will  be  the 
magnetizing  current  and  the  overload  capacity.  The  core  loss 
and  copper  loss  will  be  unchanged  and  the  heating  reduced 
because  of  the  increase  in  speed,  but  the  rating  of  the  motor  can- 
not be  increased  because  of  the  reduced  overload  capacity. 

If  the  voltage  and  frequency  both  increase  or  decrease  to- 
gether, then,  for  a  change  of  10  per  cent.,  the  characteristics  of 
the  machine  are  not  changed;  thus  it  is  possible  to  sell  440-volt 
60-cycle  motors  for  operation  on  400  volts  and  50  cycles,  with 
the  same  guarantee  in  each  case  except  that  of  heating;  the 
temperature  will  increase  due  to  the  increase  in  current  and  to 
the  decrease  in  speed. 


CHAPTER  XXXIX 
SPECIFICATIONS 

299.  The  following  is  a  typical  specification  for  a  large  induc- 
tion motor. 

SPECIFICATION  FOR  INDUCTION  MOTORS 
Type. — Squirrel-cage. 
Rating. 

Rated  capacity  in  horse-power 300 

Normal  terminal  voltage 2,200 

Phases 3 

Amperes  per  terminal  at  full-load 70  approx. 

Frequency  in  cycles  per  second 60 

Speed  at  full-load  in  revolutions  per  minute  1,160  approx. 

Construction. — The  motors  are  for  direct  connection  to  centrif- 
ugal pumps  and  shall  be  of  the  open  type,  with  split  housings  and 
bushings,  and  with  the  shaft  extended  at  both  ends  to  carry 
couplings.  The  type  of  drive  is  shown  in  the  accompanying 
sketch. 

Stator. — The  stator  coils  must  be  form  wound,  must  be  com- 
pletely insulated  before  being  put  into  the  slots,  and  must  be 
readily  removable  for  repair. 

Bidders  must  state  the  type  of  slot  to  be  used,  whether  open, 
partially  closed  or  totally  closed;  an  open-slot  construction  will 
be  given  preference. 

A  sample  coil  must  be  submitted  with  each  bid,  and  will  be 
tested  for  its  ability  to  withstand  moisture.  The  coils  put  into 
the  machine  must  conform  to  the  sample. 

Rotor. — This  shall  be  of  the  squirrel-cage  type.  All  con- 
nections in  the  electrical  circuit  shall  be  made  with  good 
mechanical  j  oints  and  shall  then  be  soldered.  The  end  connectors 
must  be  rigidly  supported  from  the  spider  and  not  merely  over- 
hung on  the  ends  of  the  rotor  bars.  All  fans  and  projecting 
parts  on  the  rotor  must  be  screened  in  such  a  way  that  a  person 
working  around  the  machine  is  not  liable  to  be  hurt. 

Workmanship  and  Finish. — The  workmanship  shall  be  first 
class.  All  parts  shall  be  made  to  standard  gauges  and  be  inter- 

422 


SPECIFIC  A  TIONS  423 

changeable.     All  surfaces  not  machined  are  to  be  dressed,  filled 
and  rubbed  down  so  as  to  present  a  smooth-finished  appearance. 

Potential  Starter. — A  suitable  potential  starter,  complete  with 
transformer  and  switches,  shall  be  supplied.  Only  one  starting 
notch  is  desired,  but  the  transformer  must  be  supplied  with  taps 
so  that  the  starter  may  be  adjusted  to  operate  with  the  smallest 
possible  starting  current.  The  switches  must  be  of  ample 
capacity  to  handle  the  starting  current.  The  starter  must  be 
provided  with  a  no-voltage  release. 

Base  and  Couplings. — The  base  shall  be  supplied  by  the  builder 
of  the  pumps.  The  couplings  shall  be  supplied  by  the  builder  of 
the  motor,  who  must  press  one-half  of  each  coupling  on  the  motor 
shaft,  and  turn,  bore,  and  key-seat  the  other  half  to  dimensions 
which  will  be  supplied  later. 

General. — Bidders  will  furnish  plans  or  cuts  with  descriptive 
matter  from  which  a  clear  idea  of  the  construction  may  be  ob- 
tained.    They  shall  also  state  the  following: 
Net  weight  of  machine  without  starter; 
Shipping  weight  of  machine  and  starter; 
Efficiency  at  ^,  f ,  full-  and  1|  load; 
Power  factor  at  J,  f ,  full-  and  1|  load; 
Air-gap  clearance  from  iron  to  iron. 

electrical  input  —  losses 

Efficiency. — This  shall  be  taken  as  -  — : — — —        — • 

electrical  input 

The  losses  to  be  used  for  the  calculation  of  the  efficiency  are: 
Windage,  friction  and  iron  loss  which  shall  be  taken  as  the 
electrical  input  determined  by  wattmeter  readings,  the  motor 
being  run  at  normal  voltage  and  frequency  and  at  no-load; 
allowance  should  be  made  for  the  copper  loss  of  the  stator 
exciting  current. 

Copper  loss  which  shall  be  found  as  follows :  The  loss  for 
different  stator  and  rotor  currents  shall  be  found  from  a  short- 
circuit  test,  the  copper  temperature  being  60°  C.,  and  the  total 
input  found  from  wattmeter  readings  being  taken  as  copper  loss. 
The  hot  stator  resistance  shall  then  be  taken  with  direct-current 
and  the  stator  copper  loss  separated  out.  The  stator  and 
rotor  currents  corresponding  to  the  different  loads  shall  be  found 
from  the  circle  diagram,  and  the  copper  losses  corresponding  to 
these  currents  found  from  the  results  of  the  short-circuit  test. 

Power  Factor. — This  shall  be  obtained  from  the  no-load  and 
short-circuit  tests. 


424  ELECTRICAL  MACHINE  DESIGN 

Overload  Capacity  and  Starting  Torque. — The  maximum  horse- 
power at  normal  voltage  and  frequency  shall  not  be  less  than 
twice  full-load,  and  the  starting  current  in  the  stator  windings 
for  full-load  torque  shall  not  exceed  five  times  full-load  current. 

Temperature. — The  machine  shall  carry  the  rated  output  in 
horse-power,  at  normal  voltage  and  frequency,  for  24  hours, 
with  a  temperature  rise  that  shall  not  exceed  40°  C.  by  ther- 
mometer on  any  part  of  the  machine,  and,  immediately  after 
the  full-load  heat  run,  shall  carry  25  per  cent,  overload  at  the 
same  voltage  and  frequency  for  2  hours,  with  a  temperature  rise 
that  shall  not  exceed  55°  C.  by  thermometer  on  any  part  of  the 
machine. 

The  temperature  rise  of  the  oil  in  the  bearings  shall  not  exceed 
40°  C.,  measured  by  a  thermometer  in  the  oil  well,  either  at  nor- 
mal load  or  at  the  overload. 

The  temperature  rise  shall  be  referred  to  a  room  temperature 
of  25°  C. 

No  compromise  heat  run  will  be  accepted.  If  the  manufac- 
turer cannot  load  the  machine,  a  heat  run  will  be  made  within  3 
months  after  erection  to  determine  if  it  meets  the  heating  guaran- 
tee, the  test  to  be  made  by  the  motor  builder  who  shall  supply 
the  necessary  men  and  instruments. 

Insulation. — The  machine  shall  withstand  the  puncture  test 
recommended  in  the  standardization  rules  of  the  American 
Institute  of  Electrical  Engineers  (latest  edition)  and  the  insula- 
tion resistance  shall  be  greater  than  one  megohm.  No  puncture 
or  insulation  resistance  test  shall  be  made  on  the  rotor. 

Testing  Facilities. — The  builder  shall  provide  the  necessary 
facilities  and  labor  for  testing  the  machine  in  accordance  with 
this  specification. 

Notes  on  Induction  Motor  Specifications. — The  characteristics 
of  an  induction  motor  are  all  more  or  less  interdependent.  A 
large  starting  torque  is  obtained  by  a  sacrifice  of  efficiency, 
and  a  large  air-gap  clearance  and  a  large  overload  capacity  by  a 
sacrifice  of  power  factor. 

The  overload  capacity  of  a  motor  should  never  be  less  than 
twice  full-load  because,  since  the  overload  capacity  is  approxi- 
mately proportional  to  the  square  of  the  applied  voltage,  a  drop 
in  voltage  of  20  per  cent,  would  cause  such  a  motor,  operating 
at  50  per  cent,  overload,  to  drop  out  of  step. 


SPECIFIC  A  TIONS  425 

300.  Effect  of  Voltage  on  the  Efficiency  and  Power  Factor.— 

If  machines  are  built  on  the  same  frame,  and  for  the  same  out- 
put and  speed,  but  for  different  voltages,  the  losses  are  affected 
in  the  following  way: 

The  windage  and  friction  loss  is  independent  of  the  voltage. 

The  iron  loss  is  unchanged  since  the  winding  is  such  that  the 
flux  per  pole  is  the  same  for  all  voltages. 

,™  ,  ,.       ,,  ,.    amp.  cond.  per  inch 

The  copper  loss  is  proportional  to  the  ratio  —  .  —  —  ~  — 

cir.  mils  per  amp. 

which  ratio  must  be  kept  constant  for  the  same  heating.     Now  the 
.    amp.  cond.  per  in.  _  amp.  2X  total  cond.2 

cir.  mils  per  amp.     ;rZ)aXcir.  mils  per  cond.  X  total  cond. 

output2 


-  — 
total  copper  section 

since  (total  cond)2  is  proportional  to  (voltage)2. 

If  then  the  total  copper  section  in  the  stator  is  the  same  at 
all  voltages  the  efficiency  is  independent  of  the  voltage,  but  if, 
as  is  generally  the  case,  the  total  section  of  stator  copper  decreases 
as  the  voltage  increases,  on  account  of  the  space  taken  up  by 
insulation,  then  in  order  that  the  copper  loss  and  heating  be  not 
too  large  the  output  of  the  machine  must  be  decreased,  and  for 
the  same  total  loss  but  a  reduced  output,  the  efficiency  of  the 
machine  is  reduced. 

The  per  cent,  magnetizing  current  =  -~ 

T> 

=  a  const.  X  —  - 
2 

Since  the  windings  for  different  voltages  are  chosen  so  as  to  keep 
the  value  of  Bg  constant,  the  per  cent,  magnetizing  current  de- 
pends largely  on  the  value  of  q.  It  was  pointed  out  above  that, 
if  wound  for  high  voltage,  the  rating  of  a  given  machine  has  to 
be  reduced  below  the  value  which  it  would  have  if  wound  for 
low  voltage.  Now  the  number  of  conductors  is  directly  propor- 
tional to  the  voltage,  and,  so  long  as  the  output  is  constant  and 
the  current  inversely  proportional  to  the  voltage,  the  product 
of  current  X  conductors  is  constant,  and  the  per  cent. 
magnetizing  current  and  the  power  factor  are  independent  of  the 
voltage.  If  the  current  drops  faster  than  the  voltage  increases, 
then  the  value  of  the  product  of  conductors  X  current  will 
decrease  and  the  per  cent,  magnetizing  current  increase,  thereby 
causing  the  power  factor  to  be  poorer,  the  higher  the  voltage. 


426  ELECTRICAL  MACHINE  DESIGN 

301.  Effect  of  Speed  on  the  Characteristics.— The  effect   of 
speed  on  the  efficiency  is  the  same  as  for  alternators  and  has  been 
studied  in  Art.  228,  page  316;  the  higher  the  speed  for  a  given  rat- 
ing, the  higher  is  the  efficiency. 

The  effect  of  speed  on  the  power  factor  and  overload  capacity 
has  been  discussed  fully  in  the  last  chapter;  the  result  of  an 
increase  in  speed  for  a  given  horse-power  is  to  improve  the  power 
factor  and  increase  the  overload  capacity. 

302.  Specifications    for    Wound -rotor    Machines. — For    such 
motors  the  same  style  of  specification  may  be  used  as  for  the 
squirrel-cage  machine,  with  the  following  modifications: 

No  potential  starter  is  required;  in  its  place  a  resistance 
starter  is  supplied  which  has  several  starting  notches.  The 
type  of  service  should  be  stated;  a  starter  to  be  used  for  variable- 
speed  work  must  be  large  because  it  absorbs  a  large  amount  of 
energy  while  in  operation,  for  example,  if  a  motor  has  to  operate 
at  half  speed  the  amount  of  heat  to  be  dissipated  by  the  starter 
is  approximately  equal  to  the  output  of  the  motor;  a  starter  that 
is  built  only  for  starting  duty  would  burn  up  in  a  short  time  if 
used  for  variable-speed  service. 

The  starting  torque  can  be  made  anything  from  zero  to  the 
pull-out  torque  by  the  variation  of  the  external  resistance  of  the 
rotor. 

The  temperature  guarantee  is  made  for  the  maximum  speed. 
A  motor  with  a  temperature  rise  of  40  deg.  cent,  at  full  load 
and  maximum  speed  can  generally  operate  continuously  at  half 
speed  with  full-load  torque  without  injury. 

When  a  wound-rotor  motor  is  operating  at  reduced  speed,  but 
with  constant  stator  current,  the  iron  loss  of  the  stator  remains 
constant,  while  that  of  the  rotor  increases  because  of  the  increase 
in  slip  and,  therefore,  of  rotor  frequency;  the  copper  losses  also 
remain  constant,  so  that  the  heating  increases  as  the  speed  de- 
creases; the  horse-power  is  not  constant  but  is  proportional 
to  the  speed. 


CHAPTER  XL 
OPERATION  OF  TRANSFORMERS 

303.  No-load  Conditions. — Fig.  262  shows  a  transformer 
diagrammatically;  the  two  windings,  which  have  Tl  and  T2 
turns  respectively,  are  wound  on  an  iron  core  C. 

An  alternating  voltage  Elt  applied  to  the  primary  coil  Tlt 
causes  a  current  Ie,  called  the  exciting  current,  to  flow  in  the  coil; 


®c, 


CVx*  V 


Is 


y2  3>c^ 

•> 

c  r 

\>c 

'f 

^ 

t  ' 

_L 

, 

c 

Ti 

-V 

J 

^ 

*.  \J 

X 

^\ 

C 

( 

V 

$ 

J    V 

•i 

Core  Type  Shell  Type 

A  B 

FIG.  262. — Diagrammalic  representation  of  transformers. 

this  current  produces  in  the  core  an  alternating  flux,  (f>co. 
The  flux  <f)co  generates  an  e.m.f.  E2  in  the  secondary  winding 
and  an  e.m.f.  E^  in  the  primary  winding,  and  to  overcome  this 
latter  voltage  the  applied  e.m.f.  must  have  a  component  which  is 


Ie 


\ 


Im 


FIG.  263. — Vector  diagram  at  no  load. 

equal  and  opposite  to  E^  at  every  instant;  the  other  component 
of  the  applied  e.m.f.  must  be  large  enough  to  send  the  exciting 
current  Ie  through  the  impedence  of  the  primary  winding. 

427 


428  ELECTRICAL  MACHINE  DESIGN 

In  Fig.  263,  which  shows  the  vector  diagram  at  no-load, 
<f>co  is  the  flux  in  the  core, 
Im  is  the  magnetizing  current,  or   that  part  of  Ie  which  is  in 

phase  with  0CO, 
Iw,   the   component   of   Ie  which  is  in  phase  with  the  applied 

e.m.f.,  is  required  to  overcome  the  no-load  losses, 
E2,  the  e.m.f.  generated  in  the  secondary  winding,  lags  <j)co  by 

90°, 
Erf,  the  generated  e.m.f.   in  the  primary   winding,    also  lags 

0CO  by  90°, 
Ei}  the  applied  e.m.f.,  is  equal  and  opposite  to  E^,  since  the 

component   required   to   overcome   the   impedence   of  the 

primary  winding  may  be  neglected  at  no-load. 
Since  E2  and  E^  are  produced  by  the  same  flux  </>co,  and  since 
Ei  =  Elb}  therefore 

f2=52  (60) 

El     Tl 

304.  Full-load  Conditions. — When  the  secondary  of  a  trans- 
former is  connected  to  a  load,  a  current  72  flows  in  the  secondary 
winding;  the  phase  relation  between  E2  and  72  depends  on  the 
power  factor  of  the  load. 

The  fluxes  which  are  present  in  a  transformer  core  at  full- 
load  are  shown  in  Fig.  262.  The  m.m.f .  between  a  and  b  =  Tlll 
ampere-turns,  where  7t  is  the  full-load  current,  and  due  to  this 
m.m.f.  a  flux  0^  is  produced  which  threads  the  primary  winding 
but  does  not  thread  the  secondary;  ^1?  is  called  the  primary 
leakage  flux  and  is  in  phase  with  the  current  7t. 

The  m.m.f.  between  c  and  d  =  T2I2  ampere-turns,  where  72  is 
the  full-load  secondary  current,  and  due  to  this  m.m.f.  the 
secondary  leakage  flux  </>2z  is  produced  which  threads  the 
secondary  winding  but  does  not  thread  the  primary. 

In  Fig.  264 

72  is  the  current  in  the  secondary  winding, 
(f>2i,  the  secondary  leakage  flux,  is  in  phase  with  72, 
(f>c,  the  flux  in  the  core,  threads  both  primary  and  secondary 

windings, 

02  is  the  actual  flux  threading  the  secondary  winding, 
E2  is  the  e.m.f.  generated  in  the  secondary  winding  by  </>2, 
E2t,  the  secondary  terminal  e.m.f.,  is  less  than  E2  by  I2R2}  the 
e.m.f.  required  to  overcome  the  resistance  of  the  secondary 
winding, 


OPERATION  OF  TRANSFORMERS 


429 


/!  is  the  current  in  the  primary  winding, 

fa,  the  primary  leakage  flux,  is  in  phase  with  I1} 

$!  is  the  actual  flux  threading  the  primary  winding, 

Elb  is  the  e.m.f.  generated  in  the  primary  winding  by  0lf 

Elt  the  primary  applied  e.m.f.,  is  made  up  of  a  component  equal 

and  opposite  to  E^,  and  a  component  7^  to  overcome 

the  primary  resistance. 


FIG.  264. — Vector  diagram  at  full  load. 


FIG.  265. — Vector  diagram  at  full  load. 

The  applied  voltage  Ei  is  constant,  and  I1R1  is  comparatively 
small  even  at  full-load,  so  that  it  may  be  assumed  that  E^ 
is  equal  to  Ely  and  that  <f>lt  which  produces  E^,  is  approxi- 
mately constant  at  all  loads;  the  resultant  of  the  m.m.fs.  of  the 
primary  and  secondary  windings  at  full-load  must,  therefore,  as 
far  as  the  primary  is  concerned,  be  equal  in  effect  to  the  m.m.f. 
of  the  exciting  current  Ie,  so  that  the  primary  current  may  be 
divided  up  into  two  components,  one  of  which  has  a  m.m.f. 


430  ELECTRICAL  MACHINE  DESIGN 

equal  and  opposite  to  that  of  the  secondary  winding,  while  the 
other  is  equal  to  Ie. 

It  is  usual  to  consider  that  the  primary  and  secondary  leakage 
fluxes  have  an  existence  separate  from  that  of  the  core  flux  </>c,- 
so  that  in  Fig.  265 

</>2  consists  of  two  components  (j>c  and  (j>2i, 
E2   consists   of  two   components;   E2C  due  to  ^c,  and  E2i  due 

to  $2i, 
E2i  lags  (f>2i  and  therefore  72  by  90°,  it  is  also  proportional  to  72, 

so  that  it  acts  exactly  like  a  reactance  and  —  I2X2,  where  X2 

is  the  secondary  leakage  reactance, 
<£t  consists  of  two  components  <j>c  and  0^, 
En  consists  of  two  components  EIC  and  E^  which  latter  =  IlXl 

the  primary  leakage-reactance  drop. 

305.  Conditions  on  Short-circuit. — On  short-circuit  the  termi- 
nal voltage  of  the  secondary  is  zero;  the  diagram  representing 


FIG.  266. — Vector  diagram  on  short  circuit. 

the  operation  is  shown  in  Fig.  266  when  the  transformer  is  short- 
circuited  and  a  primary  e.m.f.  applied  which  is  large  enough  to 
circulate  full-load  current  through  the  transformer.  Since  the 
applied  e.m.f.,  and  therefore  the  primary  flux,  is  small,  the 
exciting  current  may  be  neglected  and  TJ[^  and  T2I2  will  then  be 
equal  and  opposite. 

#i= 
where  ab  = 


OPERATION  OF  TRANSFORMERS 


431 


therefore 


R. 


_L 

i  -t 


T 

l 


where  jReg  and  Xe9  are  the  equivalent  primary  resistance  and 
reactance  respectively. 

306.  Regulation.  —  Fig.  267  shows  the  vector  diagram  at  full- 
load  with  the  primary  voltages  expressed  in  terms  of  the  secondary 
and  the  magnetizing  current  neglected. 


*3>c 


FIG.  267. — Vector  diagram  on  full  load  with  primary  voltages  expressed 
in  terms  of  the  secondary. 

The  regulation  of  constant  potential  transformers  is  defined 
as  the  per  cent,  increase  of  secondary  terminal  voltage  from  full- 
load  to  no-load;  the  primary  applied  voltage  being  constant. 

In  Fig.  267  the  rise  in  secondary  voltage  from  full-load  to 
no-load  =fc 

=  I2Re  cos  0+I2Xe  sin  d  +  bc 

where  Re  and  Xe  are  the  equivalent  secondary  resistance  and 
reactance  respectively  and 
bcX2ab=  (bd)2 


or 


bc  = 


(bd)2 
2ab 

(I2Xe  cos  6-I2Resmdy 


2(E20-bc) 
(I2Xe  cos  6-I2Re  sinfl)2 


approximately. 


432  ELECTRICAL  MACHINE  DESIGN 


The  per  cent,  regulation 

\Q/C 


=ioo/£ 

\ac, 

//   X   \  2 

=-100  —^  +  i  (  £-—  )     at  100  per  cent,  power  factor. 
- — - — -  V  approximately  at  80  per  cent. 


power  factor,  lagging  current.  (61) 


CHAPTER  XLI 
CONSTRUCTION  OF  TRANSFORMERS 

307.  Small  Core -type  Distributing  Transformers. — Figs.  268 
and  269  show  the  various  parts  of  such  a  transformer.  The 
core  A  is  built  of  L-shaped  punchings,  insulated  from  one  another 
by  varnish,  and  stacked  to  give  a  circuit  with  only  two  joints; 


FIG.  268. — Core  of  a  small  distributing  transformer. 

the  joints  are  made  by  interleaving  the  punchings  so  as  to  keep 
the  total    reluctance  of  the  magnetic  circuit  small.     The  core 
is   assembled  through  the  coils  and  is  then  clamped  together 
28  433 


434 


ELECTRICAL  MACHINE  DESIGN 


at  the  ends  by  brackets  B  and  C;  the  limbs  of  the  core  are  held 
tight  to  prevent  vibration  and  humming  by  wooden  spacers  D 
which  are  put  in  between  the  core  and  low-tension  winding. 

The  coils  are  wound  on  formers  and  are  impregnated  with 
special   compound.     In  the    example    shown  the   low-voltage 


FIG.  269. — Small  core-type  transformer. 

winding  has  two  half  coils  F  and  G  on  each  leg,  and  a  high- 
voltage  coil  H  sandwiched  between  them;  the  object  of  this 
construction  is  to  keep  the  reactance  low.  Wooden  spacers  are 


CONSTRUCTION  OF  TRANSFORMERS 


435 


used  to  separate  the  windings  from  one  another  and  from  the  core 
so  as  to  allow  the  oil  in  which  the  transformer  is  placed  to  cir- 
culate freely  and  thereby  keep  the  coils  and  the  core  cool. 

There  are  two  primary  and  two  secondary  coils,  and  the  leads 
from  each  coil  are  brought  up  through  an  insulated  board  on 
which  is  mounted  a  porcelain  block  M  for  the  high -voltage  leads; 
by  means  of  connectors  the  high-voltage  coils  may  be  put  in 


I) 


FIG.  270. — Large  shell-type  transformer. 

series  or  in  parallel.  The  four  low-voltage  leads  and  the  two 
leads  from  the  high-voltage  terminal  board  are  brought  out  of 
the  transformer  tank  through  porcelain  bushings  which  are 
cemented  in. 

The  tank  is  filled  with  a  special  mineral  oil  above  the  level  of 
the  windings,  this  oil  acts  as  an  insulator  and  also  helps  to  keep 


436 


ELECTRICAL  MACHINE  DESIGN 


the  transformer  cool  by  circulating  inside  of  the  tank  and  carrying 
the  heat  from  the  transformer  where  it  is  generated,  to  the  tank 
where  it  is  dissipated. 

308.  Large   Shell-type   Power  Transformers.— Figs.  270,  271 
and  272  show  the  various  parts  of  such  a  transformer.     The  core 


FIG.  271. — Shell-type  transformer  in  process  of  construction. 

A  is  built  up  of  punchings  which  are  insulated  from  one  another 
by  varnish  and  are  put  together  as  shown  in  Fig.  273,  with  the 
joints  overlapped  so  as  to  keep  the  total  reluctance  of  the  mag- 


CONSTRUCTION  OF  TRANSFORMERS 


437 


netic  circuit  small.  The  core  is  assembled  around  the  coils  and 
is  then  clamped  between  two  end  supports  B  and  C;  the  bottom 
one  is  supplied  with  legs  to  support  the  whole  transformer, 
while  the  top  one  carries  the  two  terminal  boards  D  and  E,  the 
former  for  the  high-voltage  leads  and  the  latter  for  those  of  the 


f    =' 


FIG.  272. — Pancake  coils  for  a  shell- type  transformer. 

low-voltage  winding.  The  core  is  sometimes  supplied  with 
horizontal  ducts  which  are  obtained  by  building  the  core  up 
with  spacers;  these  ducts  add  to  the  radiating  surface  of  the  core 
and  help  to  cool  it  but  were  not  necessary  in  the  transformer 
shown. 


438 


ELECTRICAL  MACHINE  DESIGN 


The  coils  are  wound  on  formers  and  are  then  taped  up  indi- 
vidually, after  which  they  are  gathered  together  with  the  neces- 
sary insulation  between  them  and  insulated  in  a  group;  around 
these  coils  the  core  is  built  as  shown  in  Fig.  271.  The  high- 
and  low-voltage  coils  are  sandwiched  as  shown  in  Fig.  272  to 
keep  the  reactance  small;  this  latter  illustration  also  shows  the 
method  of  insulating  the  high-  and  low-voltage  windings  from 
one  another  by  pressboard  washers  F,  and  the  two  adjacent  high- 


L/ 


FIG.  273. — Method  of  stacking  the  punchings  of  a  shell-type  transformer. 

voltage  coils  by  a  similar  but  smaller  washer  G.  The  winding 
is  well  supplied  with  ducts  through  which  the  oil  can  circulate. 
For  large  power  transformers  a  tank  such  as  that  in  Fig.  269 
has  not  sufficient  radiating  surface  and  it  is  necessary  to  use 
corrugated  tanks  or  tanks  with  extra  cooling  surface  such  as 
those  shown  in  Fig.  298  or  else  to  cool  the  transformer  by  forced 
draft  as  shown  in  Fig.  299  or  by  water  coils  as  shown  in  Fig.  300.. 
In  all  cases  the  eye  bolts  which  are  used  for  lifting  the  tanks 
should  extend  to  the  bottom  to  prevent  straining  of  the  tank 
while  it  is  being  lifted. 


CHAPTER  XLII 
MAGNETIZING  CURRENT  AND  IRON  LOSS 

309.  The  E.M.F.  Equation.— If  in  a  transformer 

(j>a  is  the  maximum  flux  threading  the  windings  at  no-load, 
T    is  the  number  of  turns  in  the  winding, 

/  is  the  frequency  of  the  applied  e.m.f .,  then  the  flux  threading 
the  windings  changes  from 

(£>a  to  —  (j)a  in  the  time  of  half  a  cycle, 
or  the  average  rate  of  change  of  flux  =  2  (j>a  X  2/ 
and  the  average  voltage  in  the  coil  =  4  T<f)aflQ  ~s 
The  effective  voltage  in  the  coil    =  average  voltage  X   form 

factor 

=  4  X  form  factor  X  T(f>aflQ  ~8 
For  a  sine  wave  of  e.m.f.,  the  form  factor  =  1.11  and 

Eeff  =  4A4:T(t>afW  ~s  volts  (62) 

310.  The  No-load  Losses. — The  losses  in  a  transformer  at  no- 
load  are  the  hysteresis  and  eddy-current   losses  in  the  active 
iron,  and  the  small  eddy-current  losses  due  to  stray  flux  in  the 
iron  brackets  and  supports;  these  latter  losses  may  be  neglected 
if  care  is  taken  to  keep  the  brackets  away  from  stray  fields. 

The  hysteresis  loss  =  KB^fW  watts,  and  the  eddy-current 
loss  =  Ke(BftyW  watts,  where 

K  is  the  hysteresis  constant  and  varies  with  the  grade  of  iron, 
Ke  is  a  constant  which  is  inversely  proportional  to  the  electrical 

resistance  of  the  iron, 

B    is  the  maximum  flux  density  in  lines  per  square  inch, 
/     is  the  frequency  in  cycles  per  second, 
t      is  the  thickness  of  the  laminations  in  inches, 
W  is  the  weight  of  the  iron  in  pounds. 

The  eddy-current  loss  =  i2r,  where  r  is  the  resistance  of  the 

eddy-current  path  and  i,  the  eddy-current  =  -» therefore  the  eddy- 

e2 

current  loss  =  — ,  where  e,  the  voltage  producing  the  eddy-cur- 
rent, is  proportional  to  the  flux  density,  the  frequency,  and  the 
thickness  of  the  iron. 

439 


440  ELECTRICAL  MACHINE  DESIGN 

The  eddy-current  loss  may  be  reduced  by  a  reduction  in  t}  the 
thickness  of  the  laminations,  but  this  reduction  cannot  be  carried 
to  extreme  because,  for  a  given  volume  of  core,  the  space  taken 
up  by  the  insulation  on  the  laminations  depends  on  their  thick- 
ness; as  they  become  thinner  the  amount  of  iron  in  the  core 
decreases,  the  flux  density  for  a  given  total  flux  increases,  and 
finally  a  value  is  reached  at  which  the  amount  of  iron  in  the 
core  is  so  small  that  the  increase  in  flux  density,  and  therefore 
in  iron  loss,  more  than  compensates  for  the  reduction  in  the  eddy- 
current  loss  due  to  the  reduction  in  the  value  of  t.  The  iron  which 
is  used  for  other  electrical  machinery  and  is  0.014  in.  thick  is 
also  that  in  most  general  use  for  transformers  up  to  frequencies 
of  60  cycles. 

Special  alloyed  iron  is  largely  used  for  60-cycle  transformers 
because  it  can  be  obtained  with  a  high  electrical  resistance  and, 
therefore,  low  eddy-current  loss,  it  has  also  a  small  hysteresis 
constant;  since  it  costs  more  and  has  lower  permeability  than 
ordinary  iron,  it  is  seldom  used  for  25-cycle  transformers  in 
which  the  core  density  is  generally  limited  by  magnetizing  cur- 
rent and  not  by  iron  loss. 

When  iron  under  pressure,  as  in  the  core  of  a  transformer  or 
other  electrical  machine,  is  subjected  to  a  temperature  of  over 
80°  C.  for  a  period  of  the  order  of  six  months,  it  will  be  found  that 
the  hysteresis  loss  has  increased  from  10  to  20  per  cent,  due  to 
what  is  known  as  ageing.  This  ageing  causes  the  iron  loss  and 
the  temperature  of  a  transformer  to  increase  and  the  efficiency  to 
decrease,  but  is  not  of  importance  in  revolving  machinery, 
because  in  such  machines  the  hysteresis  loss  is  only  a  small  part 
of  the  total  iron  loss.  Special  alloyed  iron  shows  very  little 
ageing. 

The  hysteresis  loss  in  a  transformer  is  affected  by  the  wave 
form  of  the  applied  e.m.f.  because,  as  shown  by  the  equation 

#  =  4xform  f actor X  TfaflQ-8 

for  a  given  voltage,  the  higher  the  form  factor,  the  lower  the  flux, 
the  lower  the  flux  density  and,  therefore,  the  lower  the  hysteresis 
loss.  A  wave  with  a  high  form  factor  is  peaked,  so  that  the 
advantage  of  low  hysteresis  loss  is  counteracted  by  the  fact  that 
the  peaked  e.m.f.  has  the  greater  tendency  to  puncture  the  insula- 
tion; a  sine  wave  is  the  best  for  all  conditions  of  operation. 
311.  The  Exciting  Current. — Assume  first  that  the  maximum 


MAGNETIZING  CURRENT  AND  IRON  LOSS     441 


flux  density  in  the  transformer  core  is  below  the  point  of  satura- 
tion, so  that  the  magnetizing  current  is  directly  proportional  to 
the  flux;  then,  if  the  flux  varies  according  to  a  sine  law,  the  mag- 
netizing current  also  follows  a  sine  law,  as  shown  in  diagram  A; 
Fig.  274. 

For  the  given  value  of  Bm,  the  corresponding  maximum 
ampere-turns  per  inch  of  core  may  be  found  from  Fig.  42,  page 
47,  and  the  effective  magnetizing  current  Im 

max.  amp.  turns  per  inch  X  length  of  magnetic  path 


n 


FIG.  274. — Curves  of  flux  and  magnetizing  current. 

or\/2/wT  =  max.  amp.  turns  per  in.  XL^ 
now         E  =  4A4Tcl>aflQ-* 

=  4MTBmAcflQ~8,  where  Ac   is   the   core   area   in 
square  inches 

therefore  EIm  =  &  const.  XBmX  amp. -turns  per  in.  xAcLmXf 
=  a  const.  X  function  of  BmX  core  weight Xf; 


442 


ELECTRICAL  MACHINE  DESIGN 


8        10        12    -    14        16         18        20        22        24        26        28 
Exciting  Volt  Amperes  per  Pound 

0.2       0.4      0.6       0.8       1.0      1.2       1.4       1.6       1.8       2.0       2.2      2.4      2.6       2.8 
Watts  per  Pound 

FIG.  275. — Iron  loss  and  exciting  current  in  transformers. 


MAGNETIZING  CURRENT  AND  IRON  LOSS      443 

since  amp.-turns  per  inch  depends  on  Bm  and  AcLmj  the  core 
volume,  is  proportional  to  the  core  weight;  therefore 

FT 

-^^r—     =  the  magnetizing  volt  amperes  per  pound 

=  a  function  of  BmXf 

When  the  core  is  saturated  at  the  higher  densities,  the  curve 
of  magnetizing  current  is  no  longer  a  sine  curve  but  is  peaked, 
as  shown  in  diagram  B,  Fig.  274,  because,  as  the  points  of  high 
density  are  reached,  the  current  increases  faster  than  the  flux  on 
account  of  saturation,  so  that  it  is  not  possible  to  use  the  curves 
in  Fig.  42  directly,  a  correction  factor  must  be  applied  because  of 
the  form  of  the  wave;  in  practice  a  different  method  is  followed 
which  allows  the  effect  of  joints,  saturation  and  losses  all  to  be 
taken  into  account. 

It  was  shown  that  the  magnetizing  volt  amperes  per  pound 

=  &  function  of  BmXf 
the  iron  loss  per  pound  =KfBl'6  +  Ke(Btf)2 

=  a  function  of  Bm  for  a  given  thickness 

and  frequency, 

therefore  the  exciting  volt  amperes  per  pound 
=  \/ (magnetizing  volt  amp.  per  pound) 2  +  (iron  loss  per  pound)2 
=  a  function  of  Bm  for  a  given  thickness  and  frequency. 
If  then  a  small  test  transformer  be  made  of  the  material  to  be 
used  for  a  line  of  transformers,  and  tested  at  no-load  for  exciting 
current  and  iron  loss,  the  results  may  be  plotted  against  maximum 
flux  density  as  shown  in  Fig.  275,  where  test  results  are  given  for 
ordinary  iron  and  for  special  alloyed  iron  at  25  and  at  60  cycles; 
these  curves  may  then  be  used  for  other  transformers. 

Example. — A  transformer  is  constructed  as  follows: 

Weight  of  core,  1,760  Ib.  alloyed  iron 
Turns  of  primary  winding,  526 

Output,  300  k.v.a. 

Primary  voltage,  12,000 

Frequency,  60  cycles 

Core  section,  122  sq.  in. 

<£o  =  8.6X  106  from  formula  62,  page  439 

8.6X106 
Bm  = =70,000  lines  per  square  inch 

Apparent  volt  amperes  =8X1760;  from  Fig.  275 

=  4.7  per  cent,  of  output 

Iron  loss  =  1 . 05  X  1760;  from  Fig.  275 

=  0.62  per  cent,  of  output. 


444 


ELECTRICAL  MACHINE  DESIGN 


In  the  case  of  transformers  which  have  a  butt  joint  in  the 
magnetic  circuit,  it  is  necessary  to  insulate  each  joint  with  a 
layer  of  tough  paper  0.005  in.  thick  to  keep  down  the  eddy- 
current  loss,  otherwise  the  flux  will  send  currents  across  the  face 
of  the  joint,  as  shown  in  diagram  A,  Fig.  276,  because  the  lamina- 


B 


FIG.  276. — Eddy  currents  in  transformer  joints. 

tions  generally  lie  staggered  as  shown  in  diagram  B.  In  such 
transformers  these  joints  must  be  figured  as  air-gaps  which  have 
a  thickness  of  0.005  in.  and 

max.  amp.-turns 


the  effective  amp.-turns  for  each  joint  = 


Y/2 

Bm  X  air-gap. 
Y/2X3.2 


CHAPTER  XLIII 

(  -:  .  .  .•        v 

LEAKAGE  REACTANCE 

y 

312.  Core  Type  with  Two  Coils  per  Leg. — Fig.  277  shows  the 
leakage  paths  for  a  core  type  transformer  which  has  one  primary 
and  one  secondary  coil  on  each  leg;  the  secondary  is  wound  next 
to  the  core. 


d4> 


FIG.  277. 


FIG.  278. 
FIGS.  277  and  278. — Leakage  paths  in  core-type  transformers. 

The  m.m.fs.  of  the  two  coils,  as  shown  in  Fig.  264,  are  equal 
and  opposite,  and  the  currents  are  shown  at  one  instant  by 
crosses  and  dots.  The  leakage  flux  passes  between  the  coils 

445 


446  ELECTRICAL  MACHINE  DESIGN 

and  returns  by  way  of  the  core  on  one  side,  and  through  the  air 
on  the  other  side;  the  space  S  is  like  the  center  of  a  long  thin 
solenoid,  and  the  return  path  of  the  leakage  flux  that  links  the 
primary  coil  has  an  infinite  section  so  that  its  reluctance  may  be 
neglected;  the  return  path  for  the  flux  that  links  the  secondary 
coil  is  through  the  iron  core,  and  its  reluctance  may  also  be 
neglected. 

The  m.m.f.  between  the  top  and  bottom  of  the  coils  for  dif- 
ferent depths  y  is  given  by  curve  1, 

the  m.m.f.  at  depth  y  =  T2I2  xjr  ampere-turns, 

<*2 

therefore  the  flux  d<f>  =  3.2  T272  f-  X  2nr*dy  all  in  inch  units. 

$2          Li 

This   flux  links   T.^  turns   of  the   secondary   coil,   and  the 

interlinkages  per  unit  current  =  3. 2  (  T2y  }  X^^Xdy; 

\     d2]       L 

the  coefficient  of  self-induction  of  the  secondary  coil  due  to  the 
leakage  flux  which  passes  through  the  coil 


=  3.2X    r~XT 


f*dz 

'  2  I   y*dy 

*L^ 


henry 

The  m.m.f.  along  the  space  between  coils 

=  TJi  =  T2I2  ampere-turns,  therefore  the  flux 
which  passes  between  the  coils 

=  3.  2  X  —  r-~  X  T2I2;  since  half  of  this  flux  may 
Li 

be  assumed  to  link  the  primary  and  the  other  half  the  second- 
ary coil,  the  coefficient  of  self-induction  of  the  secondary  coil 
due  to  this  flux 


henry; 
i 

the  total  coefficient  of  self-induction  of  the  secondary  coil 

=  3.2X2*rx7VXlO-8  (|  +  |)  henry; 
the  leakage  reactance  of  each  secondary  coil 


LEAKAGE  REACTANCE  447 

similarly  the  leakage  reactance  of  each  primary  coil 


and  Xe,  the  equivalent  secondary  reactance 


-*  (63) 

also  the  equivalent  primary  reactance 


If  the  coils  on  the  two  legs  are  connected  in  series  the  total 
reactance  will  have  double  the  above  value,  and  if  connected  in 
parallel  will  have  half  the  value. 

313.  Core  -type  Transformers  with  Split  Secondary  Coils.— 
Fig.  278  shows  the  leakage  paths  for  one  leg  of  such  a 
transformer. 

The  m.m.f.  between  the  top  and  bottom  of  the  coils  for  dif- 
ferent depths  of  winding  space  is  given  by  curve  1,  and  the  dis- 
tribution of  leakage  flux  is  symmetrical  about  the  line  ab. 

Consider  coil  2  and  half  of  coil  1,  the  equivalent  primary 
reactance 


and,  similarly,  for  coil  3  and  the  other  half  of  coil  1,  the  equivalent 
primary  reactance  has  the  same  value,  therefore  the  total 
equivalent  primary  reactance 


<>-•  (64) 

which  is  between  half  and  quarter  of  the  value  given  in  formula 
63,  for  the  case  where  the  coils  are  not  split  up. 

314.  Shell-type  Transformers.  —  The  coils  of  such  a  trans- 
former are  generally  arranged  as  shown  in  Fig.  272;  the  same 
arrangement  is  shown  diagrammatically  in  Fig.  279,  which  also 
shows  the  distribution  of  leakage  flux. 

The  distribution  of  leakage  flux  is  symmetrical  about  the 


448 


ELECTRICAL  MACHINE  DESIGN 


lines  a,  b,  and  c,  and  for  one  primary  and  one  secondary  coil  the 
equivalent  primary  reactance 

(65) 


\    f 

\     / 

\  S 

\    /^ 

* 

1 

«.  i 

( 

X 

Fx^ 

i 

r  1 

P 

* 

* 

i 

[ 

X 

px" 

* 

1 

—  i 

><k 

-« 

s 

> 

I- 

i  — 

L 

i 

• 

2 

1 

x 

•;x 

x\ 

y 

£ 

j|   k  *" 

^              fr     V 

^_ 

[•. 

.  «—  —  \ 

t: 

r  x 

jt 

i 

y  \ 

/  v 

J 

V  l\s   V 

a  b  *  \ 

T(  turns 

FIG.  279. — Leakage  paths  in  shell- type  transformers. 

where  MT  is  the  mean  turn  of  coil;  the  total  equivalent  primary 
reactance  when  the  primary  coils  are  all  in  series 

=  27r/X3.2xri2X^(^+|1+|2)lO-8  X  number  of  primary 

coils. 

This  gives  a  value  which  is  low;  the  error,  however,  seldom 
exceeds  6  per  cent. 


CHAPTER  XLIV 
TRANSFORMER  INSULATION 

The  insulation  of  transformers  differs  from  that  of  the  machines 
previously  discussed  in  that  it  is  submerged  in  oil. 

315.  Transformer  Oil. — Oil  has  the  following  properties  which 
make  it  valuable  for  high-voltage  insulation:  It  fills  up  all  the 
spaces  in  the  windings;  it  is  a  better  insulator  than  air  at  normal 
pressure;  it  can  be  set  in  rapid  circulation  so  as  to  carry  heat  from 
the  small  surface  of  the  transformer  to  the  large  surface  of  the 
tank;  it  has  a  fairly  high  specific  heat,  and  will  allow  the  trans- 
former immersed  in  it  to  carry  a  heavy  overload  for  a  short  time 
without  excessive  temperature  rise;  it  will  quench  an  arc. 

To  be  suitable  for  transformer  insulation  and  cooling  the  oil 
should  be  light  over  the  range  of  temperature  through  which  the 
transformer  may  have  to  operate,  because  the  ability  of  the  oil  to 
carry  heat  readily  from  the  transformer  to  the  case  or  cooling 
coils  depends  on  its  viscosity;  it  must  be  free  from  moisture, 
acid,  alkali,  sulphur,  or  other  materials  which  might  impair  the 
insulation  of  the  transformer;  it  must  have  as  high  a  flash  point  as 
is  consistent  with  low  viscosity  and  must  evaporate  very  slowly 
up  to  temperatures  of  100°  C. 

The  oil  largely  used  is  a  mineral  oil  which  begins  to  burn  at 
149°  C.,  has  a  flash  point  of  139°  C.,  a  specific  gravity  of  0.83, 
and  a  dielectric  strength  greater  than  40,000  volts  when  tested 
between  1/2-in.  spheres  spaced  0.2  in.  apart. 

The  dielectric  strength  is  greatly  reduced  by  the  additidn 
of  moisture;  0.04  per  cent,  of  moisture  will  reduce  the  dielectric 
strength  about  50  per  cent.  This  moisture  may  be  removed  by 
filtering  the  oil  under  pressure  through  dry  blotting  paper,  or, 
if  a  filter  press  is  not  available,  by  boiling  it  at  110°  C. 
until  the  dielectric  strength  has  reached  its  proper  value.  When 
a  transformer  is  in  operation  the  oil  may  be  sampled  by  drawing 
some  off  from  the  bottom  of  the  tank  through  a  tap  provided  for 
the  purpose;  the  bulk  of  the  moisture  settles  to  the  bottom. 

Only  materials  which  are  not  attacked  by  nor  are  soluble  in 
transformer  oil  should  be  used  for  transformer  insulation;  the 
29  449 


450 


ELECTRICAL  MACHINE  DESIGN 


materials  generally  used  are  cotton,  paper,  wood  and  special 
varnishes. 

Wood,  which  is  largely  used  for  spacers,  must  be  free  from 
knots,  and,  in  the  case  of  maple,  must  also  be  free  from  sugar. 
Maple  and  ash  are  largely  used,  and,  to  ensure  that  they  are  free 
from  moisture,  they  are  baked  and  then  impregnated  with 
compound,  or  are  boiled  for  about  24  hours  in  transformer  oil 
at  110°  C. 

Fullerboard  and  pressboard  are  largely  used  for  spacers  in 
transformers;  the  latter  material  has  a  laminated  structure,  so 
that  impurities  seldom  go  through  the  total 
thickness  of  the  piece,  it  also  bends  readily, 
so  that  there  is  no  objection  to  its  use  in 
sheets  1/16  in.  thick.  When  baked  and 
then  allowed  to  soak  in  transformer  oil  1/16- 
in.  pressboard  will  withstand  about  30,000 
volts. 

Only  varnishes  which  are  specially  made 
for  transformer  work  should  be  used  for  im- 
pregnating coils,  other  varnishes  may  be 
soluble  in  hot  transformer  oil. 

316.  Surface  Leakage.— Fig.  280  shows 
two  electrodes  in  air  with  pressboard  be- 
tween them.  When  the  difference  of  poten- 
tial between  the  two  electrodes  is  increased, 
streamers  will  creep  along  the  surface  of  the 
pressboard  and  finally  form  a  short-circuit 
between  the  electrodes. 

The  distribution  of  the  dielectric  flux  is 
shown  in  the  two  cases  and  in  diagram  A 
the  stress  around  the  electrodes  is  much 
larger  than  in  diagram  B.  The  mechanism  of  the  breakdown  due 
to  surface  leakage  is  not  definitely  known;  creepage  takes  place 
under  oil  as  well  as  in  air,  but  the  creepage  distance  under  oil  is 
only  about  one-third  of  that  in  air  for  the  same  test  conditions. 
The  following  tests1  were  made  on  a  sheet  of  pressboard  which 
was  dried  and  then  boiled  in  transformer  oil : 

Tested  as  in  diagram  A:  L  =  6  in.;  £  =  0.095  in.;  creepage  dis- 
tance =12. 095  in.;  voltage  to  cause  arcing  across  the  surface  = 
40,000  volts. 

1  A.  B.  Hendricks,  Transactions  of  A.  I.  E.  E.,  Vol.  30,  page  295. 


.A 
FIG. 


280. — Surface 
leakage. 


TRANSFORMER  INSULATION 


451 


Tested  as  in  diagram  B:  L  =  3  in.  =  the  creepage  distance; 
voltage  to  cause  arcing  across  the  surface  =  50,000  volts. 

Fig  281  shows  the  results  of  similar  tests  made  under  oil, 
different  thicknesses  of  pressboard  being  obtained  by  increasing 
the  number  of  sheets;  it  may  be  seen  from  the  curves  that  an 
increase  in  the  thickness  of  the  insulation  has  little  effect  on  the 
creepage  distance  between  two  electrodes  that  are  on  the  same 
side  of  the  sheet,  but  has  a  large  effect  on  the  creepage  distance 
around  the  end,  the  reason  being  that  in  the  former  case,  shown 
in  diagram  B,  the  distribution  of  stress  around  the  electrode 


160 
140 
120 
100 

:  80 
I 

60 

40 


Terminals 


an  opposite 


12345 

Total  Arcing  Distance  -  Inches 

FIG.  281. — Creepage  voltage  on  oiled  pressboard.  Conditions  of  test; 
Pressboard  0.095  in.  thick,  boiled  in  transformer  oil,  then  tested  under 
oil  for  creepage  voltage  with  the  electrodes  first  on  the  same  side  of  the 
pressboard  and  then  on  opposite  sides. 

is  almost  independent  of  the  thickness  of  the  material  on  which 
the  electrodes  rest,  while  in  diagram  A  the  dielectric  flux  passing 
through  the  material  is  inversely  proportional  to  the  thickness 
between  electrodes,  so  that  the  greater  the  thickness  the  lower 
the  stress  around  the  electrodes.  Trouble  due  to  surface  leakage 
is  often  eliminated  more  economically  by  an  increase  in  the  thick- 
ness of  the  dielectric  than  by  an  increase  in  the  creepage  length. 
317.  Transformer  Bushings.1 — The  terminals  of  the  high-  and 
low-voltage  windings  have  to  be  brought  out  of  the  tank  through 

1  A.  B.  Reynders,  Transactions  of  A.  I.  E.  E  ,  Vol.  28,  page  209. 


452 


ELECTRICAL  MACHINE  DESIGN 


bushings.  For  voltages  up  to  about  40,000  above  ground, 
bushings  made  of  porcelain  or  of  composition  are  used.  These 
bushings  extend  below  the  surface  of  the  oil  at  one  end;  the  other 
end  is  carried  above  the  tank  to  a  height  sufficient  to  prevent 
breakdown  due  to  surface  leakage. 

Fig.  282  shows  a  bushing  built  to  withstand  a  puncture  test  of 
200,000  volts  to  ground  for  one  minute.  Diagram  B  shows  the 
distribution  of  dielectric  flux  across  a  section  of  the  bushing  at 
xy,  and  since  the  strain  in  the  material  is  proportional  to  the 
dielectric  flux  density,  this  strain  is  a  maximum  at  the  surface 


1 


FIG.  282. — Solid  bushing  to  withstand  a  puncture  test  of  200,000  volts  for 

one  minute. 

of  the  conductor  and  a  minimum  at  the  outer  surface  of  the 
bushing;  the  strain  at  any  point  is  proportional  to  the  poten- 
tial gradient  at  the  point,  the  curve  of  which  is  shown. 

To  reduce  the  maximum  value  of  the  potential  gradient  it  is 
necessary  to  reduce  the  dielectric  flux  density  at  the  surface  of 
the  conductor,  which  may  be  done  by  increasing  the  diameter  of 
the  conductor  without  reducing  the  thickness  of  the  bushing,  or 
by  increasing  the  thickness  of  the  bushing. 

In  order  to  make  the  outer  layers  of  the  bushing  carry  their 


TRANSFORMER  INSULATION 


453 


proper  share  of  the  voltage,  the  condenser  type  of  bushing  shown 
in  Fig.  283  was  designed.  It  consists  of  a  number  of  concentric 
condensers  of  tin-foil  and  paper  in  series  between  the  center 
conductor  and  the  cover  of  the  tank.  When  condensers  are  put 
in  series,  the  voltage  drop  across  each  is  inversely  proportional 
to  its  electric  capacity  so  that,  in  the  condenser  type  of  bushing, 
if  each  concentric  condenser  have  the  same  thickness  and  the 


\ 


FIG.  283. — Diagrammatic  representation  of  a  condenser  bushing. 

same  capacity,  the  voltages  across  the  different  layers  will  all  be 
equal  and  the  strain  will  be  uniform  through  the  thickness  of  the 
bushing. 

The  capacity   of   such    condensers   is   proportional  to 

area  of  plates 
thickness  of  dielectric 

so  that,  if  the  thickness  of  the  different  layers  of  dielectric,  and 
also  the  area  nDL  of  the  different  layers  of  tin-foil,  be  kept  con- 


454 


ELECTRICAL  MACHINE  DESIGN 


stant,  the  voltage  across  each  thickness  of  insulation  will  be 
equal  to  the  total  voltage  divided  by  the  number  of  layers. 
A  bushing  built  with  equal  areas  of  plate  and  equal  thicknesses 
of  dielectric  has  the  shape  shown  in  diagram  B;  in  such  a  case 
the  voltages  across  the  different  layers  are  all  equal,  but  the 
distance  between  two  adjacent  layers  of  tin-foil  at  a  is  greater  than 
at  b,  so  that  the  bushing  is  not  economically  designed  for  surface 
leakage.  Condenser  bushings  are  generally  constructed  as 
shown  in  diagram  A;  the  surface  distance  between  layers  of  tin- 


D          C 
FIG.  284.— Oil  filled  bushing. 


foil   is    constant,    and   the  creepage  distance  under  oil  is  con- 
siderably less  than  in  air.  « 

When  such  a  bushing  is  in  operation,  lines  of  dielectric  flux 
pass  through  the  air  as  shown  in  diagram  B,  and  since  the  edge 
of  the  tin-foil  is  thin,  the  stress  in  the  air  at  that  edge  is 
large  and  the  air  breaks  down  there,  forming  a  corona.  The 
corona  contains  ozone  and  oxides  of  nitrogen  which  attack 
the  adjoining  insulation  and  finally  cause  breakdown  of  the 
bushing.  To  prevent  the  corona  from  forming  it  is  necessary 
to  eliminate  the  air  from  around  the  bushing,  and  for  this  purpose 


TRANSFORMER  INSULATION 


455 


the  bushing  is  surrounded  by  a  cylinder  of  fiber  shown  at  C, 
which  is  then  filled  up  with  compound. 

Another  type  of  bushing  which  is  largely  used  for  high-voltage 
work  is  the  compound  filled  bushing  of  which  a  section  is  shown 
in  Fig.  284.  This  type  of  bushing  is  built  up  of  composition 
rings  which  are  carefully  fitted  into  one  another  and  then  clamped 
between  two  metal  heads  by  a  bolt  C  which  acts  as  the  conductor. 


ff~T 


.L. 


^__i. 


Solid. 


Condenser.        Oil  Filled. 


FIG.  285. — Bushings  built  to  withstand  200,000  volts  for  one  minute. 

The  creepage  distance  is  obtained  by  building  rings  B  of  com- 
position into  the  bushing.  The  whole  center  of  the  bushing  is 
filled  with  compound  or  thick  oil  into  which  baffles  of  pressboard 
are  placed  as  shown  at  D  to  prevent  lining  up  of  impurities  in 
the  compound  along  the  lines  of  stress. 

Fig.  285  shows  a  solid  bushing,  a  condenser  bushing,  and  an  oil 
filled  bushing,  all  able  to  withstand  a  puncture  test  of  200,000 
volts  for  1  minute. 

318.  Insulation  of  Coils. — :In  most  high-voltage  shell-type 
transformers  of  moderate  output,  and  in  all  core-type  trans- 
formers, the  high -volt  age  coils  have  several  turns  per  layer,  and 
the  voltage  between  end  turns  of  adj  acent  layers,  which  is  equal 
to  the  volts  per  turn  multiplied  by  twice  the  turns  per  layer,  may 


456  ELECTRICAL  MACHINE  DESIGN 

become  high,  so  that,  while  the  cotton  coveiing  on  the  wire  is 
generally  sufficient  for  the  insulation  of  adjacent  conductors  in  the 
same  layer,  it  is  necessary  to  supply  additional  insulation  between 
adjacent  layers  of  the  coils.  It  is  also  necessary  to  provide 
sufficient  creepage  distance,  which  is  done,  where  the  space  is 
available,  by  making  the  insulation  between  layers  extend  beyond 
the  winding  as  shown  in  Fig.  288.  Where  the  space  is  not 
available,  as  in  the  coils  for  shell-type  transformers,  the  con- 
struction shown  in  diagram  A,  Fig.  287,  is  often  adopted;  one 
turn  of  cord  is  placed  at  each  end  of  each  layer  and  the  insulation 
between  layers  is  carried  out  to  cover  the  cord;  this  construction 
lessens  the  chance  of  damage  to  the  coil  while  being  handled. 

For  high-voltage  transformers  it  is  advisable  to  make  the  high- 
voltage  winding  of  a  number  of  coils  in  series  with  ample  creepage 
distance  and  ample  insulation  between  them,  and  to  limit  the 
voltage  per  coil  to  about  5000.  The  voltage  between  layers 
should  not,  if  possible,  exceed  350  volts. 

319.  Extra  Insulation  on  the  End  Turns  of  the  High-voltage 
Winding. — *A  condenser  consists  of  two  conductors  with  dielectric 
between,  so  that  the  high-  and  low-voltage  windings  of  a  trans- 
former, with  the  oil  between,  form  a  condenser;  so  also  is  there 
an  electrostatic  capacity  between  the  high-voltage  winding  and 
the  tank  and  between  the  low-voltage  winding  and  the  tank. 
A  transformer  may  therefore  be  represented  diagrammatically 
by  a  distributed  inductance  and  capacity  as  shown  in  Fig.  286. 

Suppose  that  the  transformer  is  disconnected  from  the  line  and 
all  at  the  ground  potential.  If  the  potential  of  one  end  A  of 
the  high-voltage  winding  be  suddenly  raised  to  a  value  E,  the 
potential  of  the  whole  high-voltage  winding  will  gradually  rise 
to  the  same  value.  The  potential  cannot  rise  instantaneously; 
the  voltage  at  B  for  example,  cannot  reach  the  value  E  until  the 
condensers  at  that  point  have  been  charged  to  a  value  Q  =  idt  = 
CE,  where  C  is  the  electro-static  capacity  between  point  B  and  the 
ground.  The  charging  current  i  has  to  flow  through  the  winding 
to  B,  and  this  takes  a  definite,  though  very  short,  time.  The 
condensers  near  A  will  be  charged  first  and  the  potential  above 
ground  of  each  point  in  the  high-voltage  winding  is  given  by 
curves  1,  2  and  3  at  successive  instants. 

At  the  instant  after  switching  represented  by  curve  1,  the 
difference  of  potential  between  two  points  A  and  D,  that  is, 

1  Walter  S.  Moody,  Transactions  of  A.  I.  E.  E.,  Vol.  26,  page  1173. 


TRANSFORMER  INSULATION 


457 


across  the  first  few  turns  of  the  winding,  =E1}  which  is  almost 
equal  to  the  full  potential  E;  because  of  this  high  voltage 
between  turns,  it  is  necessary  to  insulate  the  end  turns  from  one 


1  JLI-L1J.  JLJL.L-L1-L-L-L-L  1 


Low  Voltage 
Winding 


Voltage 
nding 


TTTTTTTTTTTTTTTTT 


FIG.  286. — The  potential  of  transformer  coils  immediately  after  switching. 


0.02  Fuller-board- 

0.014"Fuller-board^ 
0. QQI'F  u  1 1  e  r-  boa  rd  ^ 
Cord  — 

D.C.C.  Square  Wire 
V2  Lap  Tape s 


i  urn  i  an 


0.014  Fuller-board 

—Wire  with  Two 
Wrappings  of 
Empire  Cloth  Tape 


Wire  with  One 
Wrapping  of  Tape 

0.007"Fuller-board 
l/2    LaP  Tape 


A  B 

FIG.  287. — Insulation  of  the  end  turns  of  a  12,000  volt  transformer  coil, 
another  for  a  voltage  between  turns  of  many  times  the  normal 


value. 


Any  sudden  change  in  the  potential  of  a  transformer  terminal. 


458 


ELECTRICAL  MACHINE  DESIGN 


such  as  that  due  to  switching  or  to  grounding  of  a  line,  will 
produce  this  high  voltage  between  end  turns. 

Diagram  A,  Fig.  287,  shows  a  method  of  insulating  the  end 
turns  of  a  coil  for  a  shell-type  transformer,  when  the  coil  is  of 
wire  wound  in  layers,  and  diagram  B,  for  a  coil  wound  with  strip 


HV. 


sUl.c.c.  wire 


=.014  'Fuller-board 
between  Layers 


0.02  Micanite 
0.10'fcress-  board 


}4  Lap  Cotton  Tape 

Coils  are 
Impregnated 


FIG.  288. — Insulation  for  a  2200/220  volt  transformer. 

copper.  This  extra  insulation  is  put  on  each  end  of  the  high- 
voltage  winding  for  a  distance  of  about  75  ft.,  and  then  any  taps 
that  are  required  for  the  purpose  of  changing  the  transformer 
ratio  are  connected  to  the  inside  of  the  winding,  so  that  the 
extra  insulation  is  always  on  the  end  turns. 


TRANSFORMER  INSULATION 


459 


r^f 

¥fc 

—  —  P?-| 

M^ 

sO 

-*s*--> 

--.  :    '- 

{  •"'"-' 

^^ 

t 

L^ 

kk        „„,    ^  j 

FIG.  289. — Insulation  for  a  shell-type  transformer. 


140 


120 


100 


&GO 


40 


20 


7® 


'/ 


12345 

Values  from  Curves  1  and  2  in  Inches 
5        10         15 
Values  from  Curve  3  in  Tnches 

FIG.  290. — Spacings  for  the  coils  of  shell-type  transformers. 


460 


ELECTRICAL  MACHINE  DESIGN 


320.  Insulation  between  the  Windings  and  Core. — Fig.  288 
shows  the  method  of  insulating  a  small  core-type  distributing 
transformer  wound  for  2200/220  volts. 

Fig.  289  shows  an  example  of  a  shell-type  transformer  wound 
for  moderate  voltage,  an  illustration  of  such  a  winding  and 
insulation  is  shown  in  Figs.  271  and  272.  The  various  spacings 
used  for  different  voltages  are  given  in  Fig.  290,  where  curve  1 
gives  the  distance  between  high-  and  low-voltage  windings  and 
also  between  the  high-voltage  winding  and  the  core;  curve  2  gives 


'//  \ 

Pressboard    L.Y  Coils 


\ 

H.V.  Coils 

Insulation 

FIG.  291. — Insulation  for  110,000  volts. 

the  total  thickness  of  the  pressboard  in  this  distance;  curve  3 
gives  the  distance  X  between  the  high-voltage  coil  and  the  iron 
at  the  top  and  bottom  of  the  core. 

Fig.  291  shows  an  example  of  a  shell-type  transformer  wound 
for  63,500/13,200  volts  for  operation  in  a  Y-connected  bank  on 
110,000  volts;  the  insulation  to  ground,  and  also  from  high- 
to  low-voltage  winding,  is  the  same  as  that  for  a  110,000-volt 
transformer.  One-quarter  of  the  total  winding  is  shown  in 
plan;  there  are  12  high-voltage  coils,  so  that  the  voltage  per  coil 
=  5300. 


CHAPTER  XLY 
LOSSES,  EFFICIENCY  AND  HEATING 

321.  The  Losses. — The  losses  in  a  transformer  are:  the  iron 
loss,  the  loss  in  the  dielectric,  and  the  copper  loss. 

The  iron  loss  has  already  been  discussed  in  Art.  310,  page  439. 

The  loss  in  the  dielectric,  about  which  very  little  is  known, 
causes  the  material  to  heat  up  and  its  dielectric  strength  to 
decrease.  The  loss  is  kept  small  by  the  use  of  ample  distances 
between  points  at  different  potential,  and  the  heating  is  kept 
small  by  a  liberal  supply  of  oil  ducts  through  the  insulation; 
the  layers  of  solid  insulation  should  not  be  thicker  than  0.25  in. 

322.  The  Copper  Loss. 

If  MT  is  the  mean  turn  of  a  transformer  coil  in  inches, 
M  is  the  section  of  the  wire  in  the  coil  in  circular  mils, 
I  is  the  effective  current  in  each  turn  of  the  coil, 

MT 

then  the  resistance  of  each  turn  =  -^-  ohms 

M 

MTxP 
and  the  loss  per  coil  in  watts      = — -^ — X  turns  (65) 

In  addition  to  the  above  copper  loss  there  is  the  eddy-current 
loss  in  the  conductors,  which  may  be  large  if  the  conductors  are 
not  properly  laminated  or  arranged  so  that  the  leakage  flux  cuts 
their  narrow  sides.  Diagram  B,  Fig.  292,  shows  part  of  the 
winding  of  a  core-type  transformer  and  the  direction  of  the  alter- 
nating leakage  flux  at  one  instant.  If  the  coils  are  wound  of 
strip  copper  on  edge  as  shown  at  E,  then  eddy  currents  will  flow 
in  the  direction  shown  by  the  crosses  and  dots,  and  the  loss  will 
be  much  larger  than  if  the  coils  are  wound  with  flat  strip  as 
shown  at  A. 

Diagram  D,  Fig  292,  shows  part  of  the  winding  of  a  shell-type 
transformer,  and  the  direction  of  the  leakage  flux  and  the  eddy 
currents  at  one  instant.  If  such  a  coil  is  laminated  in  the  direc- 
tion of  the  leakage  lines  it  will  be  weakened  mechanically;  for 
that  reason  it  is  not  advisable  to  laminate  the  conductors  unless 

461 


462 


ELECTRICAL  MACHINE  DESIGN 


they  are  wider  than  0.5  in.  for  60  cycles,  or  0.75  in.  for  25  cycles, 
for  which  values,  and  for  ordinary  current  densities,  the  eddy- 
current  loss  will  be  about  20  per  cent,  of  the  calculated  PR  loss. 
Even  after  the  conductors  of  a  core-type  transformer  have  been 
laminated,  considerable  eddy-current  loss  may  under  certain 
circumstances  be  found  in  the  windings;  for  example,  A,  Fig. 
292,  shows  part  of  the  winding  of  a  low-voltage  large-current 
transformer  where  the  coil  is  made  up  of  four  wires  in  parallel; 
eddy  currents  tend  to  flow  in  the  direction  represented  at  one 


FIG.  292. — Eddy  currents  in  transformer  coils. 

instant  by  the  crosses  and  dots,  and  since  the  parallel  wires 
are  all  connected  together  at  the  ends,  the  current  will  flow  down 
one  wire  a,  cross  through  the  soldered  joint  at  the  end  to  wire  b, 
up  which  it  will  pass  and  then  return  by  the  other  soldered  joint 
to  conductor  a,  so  that  if  the  coil  is  developed  on  to  a  plane  the 
currents  will  flow  as  shown  in  diagram  C.  To  eliminate  this 
circulating  current  the  bunch  of  wires  is  given  a  half  twist,  as 
shown  at  F,  so  that  in  any  one  strip  there  are  two  e.m.fs., 
produced  by  the  leakage  flux,  which  are  equal  and  opposite, 
the  resultant  e.m.f.  is  therefore  zero  and  no  circulating  current 
will  flow. 


LOSSES,  EFFICIENCY  AND  HEATING          463 

323.  The  Efficiency. 

If  C.L.  is  the  iron  or  core  loss  in  watts, 
PR    the  copper  loss  in  watts, 
El     the  output  of.  the  transformer  in  watts, 

„  .  output 

then,  in,  the  efficiency  =—  -—*  — 

output  +  losses 

El 
EI+PR+C.L. 

The  efficiency  is  a  maximum  when 


or  (EI  +  PR  +  C.L.)E-EI(E  +  2IR)=Q 

or  PR  =  C.L. 

that  is,  when  the  copper  loss  is  equal  to  the  core  loss. 

The  all-day  efficiency,  which  is  of  importance  in  distributing 
transformers,  is  defined  by  the  following  equation: 

EIXX 
all-day  efficiency  = 


where  X  is  the  number  of  hours  during  which  the  transformer  is 
loaded  each  day,  and  24  is  the  number  of  hours  during  which  the 
iron  loss  is  supplied.  Distributing  transformers  should  therefore 
be  designed  to  have  as  small  a  core  loss  as  possible,  because  this 
loss  has  to  be  supplied  continuously. 

324.  Heating  of  Transformers.  —  Since  nearly  all  except  instru- 
ment transformers  are  oil  immersed,  the  subject  of  cooling  by 
natural  draft  is  not  of  importance  and  shall  not  be  discussed. 

When  a  transformer  is  in  operation  under  oil  the  heat  generated 
in  the  core  and  windings  has  to  be  carried  to  the  tank,  from  the 
external  surface  of  which  it  is  dissipated  to  the  air.  When  the 
oil  in  contact  with  the  transformer  surface  is  heated,  it  be- 
comes lighter  and  rises,  and  cool  oil  flows  in  from  the  bottom  of 
the  tank  to  take  its  place,  so  that  a  circulation  of  oil  is  set  up, 
as  shown  in  Fig.  293.  That  it  may  circulate  freely  the  oil  should 
have  a  low  viscosity,  and  the  lighter  the  oil  the  better  it  is  as  a 
cooling  medium  for  transformers. 

325.  The  Temperature  Gradient  in  the  Oil.—  Fig.  293  shows  a 
core-type  transformer  and  also  shows  the  temperature  of  the  oil 
at  different  points  along  its  surface.     At  the  bottom  of  the  tank 
the  oil  temperature  is  T^;  the  oil  moves  along  the  circulation 
path  and  its  temperature  rises  and  reaches  a  maximum  value  Tt 


464 


ELECTRICAL  MACHINE  DESIGN 


at  the  top  of  the  transformer,  it  then  passes  to  the  tank  and, 
as  it  moves  downward,  the  heat  is  gradually  given  up  to  the  tank. 
After  a  number  of  hours,  during  which  the  whole  body  of  the 
transformer  and  the  oil  are  absorbing  heat  and  being  raised  in 
temperature,  conditions  become  fixed,  the  oil  circulation  and 
its  temperature  cycle  become  definite,  and  the  different  points 
of  the  transformer  have  their  maximum  temperature. 

326.  The  Temperature  Gradient  in  a  Core-type  Transformer.— 
Consider  the  core  of  the  transformer  shown  in  Fig.  293.  Iron  is 
a  good  conductor  of  heat  along  the  laminations,  so  that  the 
difference  in  temperature  between  the  points  A  and  B  of  the 


FIG.  293. — Temperature  gradient  in  a  core-type  transformer. 

core  cannot  be  great,  and  the  difference  in  temperature  between 
the  core  and  the  adjacent  oil  must  be  greater  at  the  bottom  of 
the  core  than  at  the  top;  because  of  this,  much  of  the  heat 
generated  in  the  top  part  of  the  core  is  conducted  downward 
and  dissipated  from  the  surface  at  the  bottom,  that  is,  the 
bottom  part  of  the  core  surface  is  more  active  than  the  top  part 
in  dissipating  the  heat  due  to  the  iron  losses. 

The   conditions   are   different  for  the  windings.     These   are 
formed  of  insulated  wire  wound  in  layers,  and,  because  of  the 


LOSSES,  EFFICIENCY  AND  HEATING 


465 


number  of  layers  of  insulation  in  the  length  of  the  coil,  very 
little  of  the  heat  generated  in  the  top  turns  will  be  conducted 
downward  through  the  winding.  Most  of  the  heat  generated  at 
any  point  in  the  winding  will  be  conducted  to  and  dissipated 
from  the  nearest  coil  surface,  so  that  the  watts  dissipated  per 
unit  area  of  coil  surface,  and  therefore  the  temperature  difference 
between  the  coil  surface  and  the  adjacent  oil,  will  be  approxi- 


Oil  Level 


B 


FIG.  294. — Shell-type  transformer  in  tank. 

mately  constant  at  all  points,  and  the  temperature  of  the  surface 
of  the  coil  will  be  a  maximum  at  the  top  of  the  transformer. 
The  hottest  part  of  the  whole  winding  will  be  at  C. 

Measurement  of  the  temperature  rise  by  resistance  gives  little 
information  as  to  the  temperature  of  the  hottest  part  of  the  coil 
of  a  core-type  transformer,  because  the  temperature  so  found 
is  the  average  temperature  and  may  be  less  than  that  of  the  oil 
measured  at  the  top  of  the  transformer. 

327.  The  Temperature  Gradient  in  a  Shell -type  Transformer.— 
Fig.  294  shows  such  a  transformer.  Since  the  core  is  laminated 
horizontally,  and  since  iron  is  a  poor  conductor  of  heat  across  the 
laminations,  most  of  the  heat  generated  at  any  point  in  the  core 
is  conducted  to  and  dissipated  from  the  nearest  core  surface,  so 
that  each  part  of  the  core  surface  is  equally  active  in  dissipating 

30 


466 


ELECTRICAL  MACHINE  DESIGN 


heat,  and  the  temperature  of  the  core  is  a  maximum  at  the  top 
and  a  minimum  at  the  bottom. 

The  conditions  are  different  for  the  windings.  These  are 
made  up  of  what  are  known  as  pancake  coils,  which  are  thin  and 
have  a  large  radiating  surface.  Since  the  top  layers  of  the 
winding  at  A  are  connected  directly  to  the  bottom  layers  at  B 
by  a  short  length  of  copper,  the  temperature  difference  between 


o.i 


0.2  0.3 

Watts  per  Sq.  In.  Barrel  Surface 


FIG.  295. — Heating  curves  for  transformer  tanks. 


A  and  B  cannot  be  very  great,  and  the  difference  in  temperature 
between  the  winding  and  the  adjacent  oil  must  be  greater  at  the 
bottom  than  at  the  top.  Because  of  this  much  of  the  heat 
generated  in  the  top  part  of  the  winding  is  conducted  downward 
and  dissipated  from  the  winding  surface  at  the  bottom  of  the  coil. 
The  temperature  of  the  winding  is  more  uniform  throughout 
than  in  a  core  type  transformer,  and  resistance  measurements 
are  of  more  value. 
328.  The  Temperature  of  the  Oil. — The  rise  in  temperature  of 


LOSSES,  EFFICIENCY  AND  HEATING 


467 


the  oil  over  that  of  the  external  air  depends  principally  on  the 
loss  to  be  dissipated,  and  on  the  external  surface  of  the  tank. 

The  heat  in  the  oil  is  transmitted  through  the  tank  and 
dissipated  from  its  external  surface.  Part  of  this  heat  is  dissi- 
pated by  direct  radiation,  and  part  by  convection  currents  which 
flow  up  the  sides  of  the  tank.  For  a  plain  boiler-plate  tank, 
without  ribs  or  corrugations,  the  highest  temperature  rise  of  the 


FIG.  296. — Corrugated  tank. 

oil  is  plotted  against  watts  per  square  inch  external  surface  in 
Fig.  295,  for  a  tank  which  is  round  in  section,  and  which  has  a 
height  of  approximately  1.5  times  the  diameter.  This  tempera- 
ture rise  is  made  up  principally  of  the  temperature  difference 
between  the  air  and  the  tank,  and  that  between  the  tank  and  the 
oil;  the  former  is  about  three  times  as  large  as  the  latter. 

The  temperature  rise  of  the  oil  may  be  reduced  by  increasing 


468 


ELECTRICAL  MACHINE  DESIGN 


the  surface  of  the  tank  which  is  readily  done  by  making  it 
corrugated,  as  shown  in  Fig.  296.  This  increase  in  surface  does 
not  increase  the  direct  radiation  from  the  tank,  because  only  that 
component  of  surface  which  is  perpendicular  to  a  radius  is 
effective;  for  this  reason  the  watts  per  square  inch  for  a  given 
temperature  rise  does  not  increase  directly  as  the  increase  in 
surface.  Consider  the  curve  in  Fig.  295  for  corrugations  3  in. 
deep  and  spaced  1  in.  apart;  the  external  surface  of  the  tank  is 


Pipe  Surface   7500  sq.  in, 
Tank  Surface  4100  sq.  in 


0.3          0.4  0.5          0.6 

Watts  per  Sq.  Inch 

FIG.  297. — Heating  curves  for  transformer  tanks. 

increased  about  six  and  one-half  times,  while  the  watts  per 
square  inch  for  a  given  temperature  rise  is  only  increased  about 
60  per  cent,  over  the  value  for  a  plain  boiler-plate  tank. 

Fig.  297  shows  the  results  of  tests  on  a  boiler-plate  tank  with 
external  pipes  added  to  improve  the  circulation.  It  will  be 
seen  from  curves  1  and  2  that  the  watts  per  square  inch  of 
total  surface  for  a  given  temperature  rise  is  almost  as  large  in 


LOSSES,  EFFICIENCY  AND  HEATING 


469 


the  special  tank  as  in  the  plain  boiler-plate  tank  or,  comparing 
curves  1  and  3,  the  surface  of  the  special  tank  is  2.8  times  that 
of  the  plain  boiler-plate  tank,  while  the  watts  per  square  inch  for 
a  given  temperature  rise  is  increased  about  2.5  times. 

Fig.  298  shows  a  tank  built  so  as  to  present  three  cooling 
surfaces  to  the  air. 


Oil  Level 


FIG.  298. — Tank  with  large  cooling  surface. 


329.  Air-blast  Transformers. — Fig.  299  shows  such  a  trans- 
former. The  problem  in  this  case  is  like  that  discussed  fully  on 
page  281  on  the  heating  of  turbo  generators;  150  cu.  ft.  of  air 
is  supplied  per  minute  per  k.w.  loss,  and  the  average  temper- 
ature of  the  air  increases  about  12  deg.  cent,  between  the  inlet 
and  outlet.  The  temperature  of  the  coils  and  core  is  kept 
within  reasonable  values  by  providing  the  necessary  radiating 
surface,  using  the  formula, 

watts  per  square  inch  for  1  deg.  cent,  rise  =  0.0245(1  +0.00127  7), 

where  the  temperature  rise  is  measured  on  the  surface  and  V  is 
the  velocity  of  the  air  across  the  surface  in  feet  per  minute. 
In  the  case  of  vent  ducts,  and  surfaces  which  are  facing  one 
another,  it  must  be  noted  that  there  can  be  no  radiation  term 


470 


ELECTRICAL  MACHINE  DESIGN 


because  the  surfaces  are  at  the  same  temperature  and  in  such 

cases, 

watts  per  square  inch  for  1  deg.  cent,  rise  =0.0245(0.001277). 

The  air  used  should  be  filtered,  otherwise  the  ducts  will 
become  clogged  up  with  dust  and  the  transformer  get  hot. 
Dampers  are  usually  supplied  at  the  top  of  the  case  so  that 
the  distribution  of  the  air  through  the  core  and  coils  may  be 
controlled. 


FIG.  299. — Air  blast  transformer. 

330.  Water-cooled  Transformers. — If  coils  of  copper  pipe 
carrying  water  be  placed  at  the  top  of  the  case  as  shown  in  Fig. 
300,  then  the  oil  which  is  heated  by  contact  with  the  transformer 
will  rise  and  carry  the  heat  to  the  cooling  coils. 

If  ti  is  the  inlet  temperature  of  the  water, 

t0   is  that  at  the  outlet, 

then  each  pound  of  water  passing  through  the  coils  per  minute 
takes  with  it  (t0  —  ti)  Ib.  calories  per  minute 
or  32(t0-ti)  watts. 

With  2.5  Ib.  of  water  per  minute  per  kilowatt  loss  the  average 
temperature  rise  of  the  water  will  be  12.5  deg.  cent. 


LOSSES,  EFFICIENCY  AND  HEATING          471 

It  is  advisable  in  water-cooled  transformers  to  immerse  the 
whole  of  the  cooling  coil,  otherwise,  due  to  the  low  temperature 
of  the  water  passing  through,  moisture  will  deposit  on  the  coil 
and  get  into  the  oil.  The  coil  should  be  of  seamless  copper  tube 
about  11/4  in.  external  diameter,  and  the  drain  tap  should  be 


FIG.  300. — Water  cooled  transformer. 


at  the  bottom  of  the  spiral  so  that,  when  not  in  operation,  the 
spiral  will  be  empty  and  therefore  will  not  burst  in  frosty  weather. 
331.  Heating  Constants  used  in  Practice. — The  calculation  of 
the  temperature  rise  of  a  transformer  is  so  complicated  by  the  oil 
circulation,  and  by  the  temperature  gradient  in  the  oil,  coils  and 


472 


ELECTRICAL  MACHINE  DESIGN 


core  that,  until  the  results  of  a  complete  investigation  of  the 
subject  are  available,  empirical  constants  will  have  to  be  used. 

The  necessary  tank  surface  for  a  given  loss  is  found  from  Fig. 
295. 

The  watts  per  square  inch  coil  surface 
=  0.35  for  self-cooled  shell-type  coils  wound  with  small  wire 
=  0.4    for  self-cooled  shell-type  coils  wound  with  strip  copper 
=  0.35  for  small  core-type  transformers;  these  figures  may  be 

increased   20   per    cent,    for    trans- 
formers which  are  water  cooled  or 

I     & 

cooled  by  forced  draft. 

The  watts  per  square  inch  iron 
surface 

=  1.0  for  both  core  and  shell  type; 
the  area  of  cooling  surface  is  taken 
as  the  edge  surface  and  half  of  that 
part  of  the  flat  surface  which  is  ex- 
posed to  the  oil  circulation,  see  Art. 
332. 

The  watts  per  square  inch  water 
pipe  surface 

=  1.0,  for  a  1.25-in.  pipe,  the  sup- 
ply being  2.5  Ib.  per  minute  per  k.w. 
loss. 

332.  Effect  of  Ducts. — It  is  difficult 
to  determine  how  effective  the  ducts 
are  in  keeping  a  transformer  core  cool.  Fig.  301  shows  a  block 
of  iron  which  is  laminated  vertically.  The  hottest  part  of  the 
iron  is  at  A  and  the  temperature  difference  from  A  to  B. 


*Tf 

i 

I 

C 

i  t 

A 

FIG.  301. — Heat  paths  in  a 
transformer  core. 


j. 

=  (watts  per  cu.  in.) -5-  deg.  cent;  page  105 

o 

that  between  A  and  C 

=  Tac 

=  (watts  per  cu.  in.)—    -  deg.  cent. 

o 

The  temperature  difference  between  surface  B  and  the  oil 

=  (watts  per  cu.  in.)  Y  X 16 
since  the  temperature  difference  between  the  iron  and  the  adjoin- 


LOSSES,  EFFICIENCY  AND  HEATING          473 

ing  oil  is  16  deg.  cent,  per  watt  per  square  inch.     The  tempera- 
ture difference  between  surface  C  and  the  oil 

=  (watts  per  cu.  in.)XXl6 

The  relative  heat  resistance  of  the  two  paths  may  be  taken 
approximately  as 


pathB 


If  the  ducts  are  spaced  2  in.  apart,  so  that  X  =  1.0  in.,  then  for 
different  values  of  Y  the  relative  heat  resistance  may  be  found 
from  the  following  table: 

RELATIVE   HEAT  RESISTANCE 

X  Y  Along  laminations  Across  laminations 

1  in.  1  in.                   0.48                               1.0 

1  in.  2  in.                   1.0                                 1.0 

1  in.  Sin.                   1.5                                 1.0 

1  in.  4  in.                   2.0                                 1.0 

that  is,  for  the  particular  values  taken,  the  duct  surface  is  half  as 
effective  as  that  of  the  edge,  if  it  is  as  well  supplied  with  cool  oil, 
that  is,  if  the  ducts  are  vertical  and  of  sufficient  width  to  allow 
free  circulation. 

333.  The  Maximum  Temperature  in  the  Coils.  —  Although  the 
maximum  temperature  in  the  coils  of  a  transformer  cannot  readily 
be  determined,  it  is  necessary  to  find  out  on  what  it  depends  and 
what  its  probable  value  may  be. 

In  Fig.  302,  which  shows  part  of  the  coil  of  a  transformer,  let 
the  thickness  of  the  coil  be  small  compared  with  the  mean  turn 
MT,  and  assume  that  the  heat  passes  in  both  directions  from  the 
center  line  L. 

If,  of  the  thickness  x,  the  part  kx  is  insulation  and  (1—  k)  x  is 
copper  then  the  current  in  the  section  xy 

=  xy(l-k)  X  amperes  per  square  inch 


sq.   n.  per  amp. 
xy  (l-fc)X  1.27X106 
cir.  mils  per  amp. 


474 


ELECTRICAL  MACHINE  DESIGN 


The  resistance  of  a  ring  of  length  MT  and  section  z?/(l-A;)  sq.  in. 

= MT. 

~xy  (l-/b)Xl.27xl06 
the  loss  in  this  ring  =  current2  X  resistance 

(xy  (1-&)X1.27X106)2XM'T. 


xy  (l-fc)Xl.27xl08  (cir.  mils  per  amp.)2 

=  MTX  xy  (1  -  k)  X  1.2.7  X  106 
(cir.  mils  per  amp.)2 

The  heat  due  to  this  loss  crosses  the  section  of  thickness  dx, 
of  which  A;  X da;  is  insulation,  and  since  the  specific  conductivity  of 


\dx 


A  B 

FIG.  302. — Part  of  a  transformer  coil  showing  insulation  between  layers. 


insulating  material  =  0.003,  in  watts  per  inch  cube  per  deg.  cent, 
difference  in  temperature,  therefore  the  difference  in  tempera- 
ture between  the  center  and  the  surface 


-Jr-J: 


M Txxy(l  - k]  X  1.27X  106      kXdx_ 

/N     TI  *-  rrt  v     ,  *?\ 


(cir.  mils  per  amp.) 
2.1  XlO8  k(l-k)X2 


0.003 


(66) 


(cir.  mils  per  amp.)2 

Consider  the  following  example:  A  core-type  transformer  with 
the  windings  insulated  as  in  Fig.  288,  has  the  high-tension  winding 
made  with  No.  12  square  d.  c.  c.  wire.  The  high- voltage  winding 
is  1  in.  thick,  the  current-  density  is  1600  cir.  mils  per  ampere, 
and  there  is  one  thickness  of  0.007  in.  fullerboard  between  layers; 


LOSSES,  EFFICIENCY  AND  HEATING          475 

it  is  required  to  find  the  maximum  difference  in  temperature 
between  the  inner  and  outer  layers  of  the  winding. 

Thickness  of  wire  =  0  .  0808 

Thickness  of  cotton  covering  =0.01 
Thickness  of  fuller-board  =  0  .  007 

Value  of* 


Value  of  l-k  -0.89 

,.~  2.1X108XO.  174X0.89 

Temperature  difference  =—          —  Ignn2 

JLoUU 

=  13  deg.  cent. 

If  round  wire  is  used  instead  of  square,  then  the  contact  area 
between  adjacent  layers  is  greatly  reduced,  and  the  tempera- 
ture difference  increased.  It  is  advisable  for  such  coils  as  that 
discussed  above  to  use  square  or  rectangular  wire  and  to  limit 
the  thickness  of  the  coil  to  1  in.,  and  the  current  density  to  about 
1600  cir.  mils  per  ampere. 

334.  The  Section  of  the  Wire  in  the  Coils.—  Diagram  A,  Fig. 
302,  shows  part  of  a  coil  of  a  shell-type  transformer,  and  B 
shows  part  of  a  coil  of  a  core  type  transformer. 

The  loss  in  one  layer  of  the  winding,  as  may  be  seen  from  the 
last  Art. 


MTx2Xy(l  -  fe)  X  1.27X  106 


6        ttg 
(cir.  mils  per  amp.)2 


the  corresponding  radiating  surface  =MTXr  sq.  in. 
therefore  the  watts  per  sq.  in.   = 


-  —    .         , 

2X  (cir.  mils  per  amp.)2 

and  cir.  mils  per  amp.  =  8XlOaJ     2X<l~k^  (67) 

\watts  per  sq.  in. 

=  1350^2^(1  -k)2  when  watts  per  sq.  in.  -0.35 
=  1260\/2X(1-A;)2  when  watts  per  sq.  in.  =  0.4 


CHAPTER  XL  VI 
PROCEDURE  IN  DESIGN 

335.  The  Output  Equation. 

#  =  4.447Ya/10-8,  formula  62,  page  439; 
and  El  =  the  watts  output 


4A</>a2      /•     -irk  7       0a     magnetic  loading 

=  4.44vy^-X/XlO~8  where  kt  =  ^,°  =  -^-^—,  —  T^ 
kt  TI      electric  loading 

The  volts  per  turn  of  coil  =  Vt 

=  4.44<£a/10~8 


so  that,  for  a  given  voltage,  the  lower  the  frequency  the  larger 
the  product  (f>a XT.  If  a  transformer  is  built  with  a  large 

number  of  turns,  so  that  fcj  =  ™~  is  small,  then  the  copper  loss 

is  large  because  of  the  large  number  of  turns,  and  the  core  loss 
is  small  because  of  the  low  frequency;  such  a  transformer  would 
therefore  have  its  maximum  efficiency  at  a  fraction  of  full-load; 
see  page  463.  In  order  that  the  efficiency  may  be  a  maximum  at 
or  near  full-load,  the  full  load  copper  and  the  core  loss  must  be  ap- 
proximately equal  and  the  flux  must  increase  as  the  frequency 

decreases;  it  is  found  in  practice  that  the  value  of  kt=^  is 

approximately  inversely  proportional  to  the  frequency,  or  that 
ktf  is  approximately  constant,  therefore 

volts  per  turn,  Vt  =  B,  const.  X  \/watts  (68) 

where  the  following  average  values  of  the  constant  are  found 

in  practice;  —  for  core-type  distributing  transformers 

oU 

•^  for  core-type  power  transformers 
o(J 

^  for  shell-type  power  transformers. 
4d 

The  constant  for  the  distributing  transformer  is  less  than  that 

476 


PROCEDURE  IN  DESIGN 


477 


for  the  power  transformer  because,  while  in  the  latter  the  highest 
efficiency  is  desired  around  full-load,  in  the  former  a  small  core 
loss  and  a  high  all  day  efficiency  is  desired.  To  obtain  a  small 

core  loss  it  is  necessary  to  keep  the  value  of  kt=  —small,  and 

therefore  the  constant  in  formula  68  must  be  small. 

The  constant  is  different  for  core-  and  for  shell-type  trans- 
formers because  of  the  difference  in  construction.  Fig.  303 
shows  the  ordinary  proportions  of  a  core-type  transformer;  the 


J L 


J        L 

A 


FIG.  303. — Core-type  transformer.      FIG.  304. — Shell-type  transformer. 

distance  a  is  generally  about  1.5X6  so  as  to  keep  the  ratio  of 
X  to  Y  within  reasonable  limits,  and  prevent  the  use  of  a  thin 
wide  tank. 

If  the  coil  on  limb  B  of  the  transformer  in  Fig.  303  be  placed  on 
limb  A,  and  limb  B  then  split  up  the  center  and  one-half  bent 
over  to  give  Fig.  304,  a  shell-type  transformer  is  produced  which 
has  the  same  amount  of  copper  and  iron  as  the  corresponding 
core-type  transformer.  The  resulting  shell-type  transformer  is 
flat  and  low,  so  that  the  tank  required  to  hold  it  takes  up  con- 


478 


ELECTRICAL  MACHINE  DESIGN 


siderable  floor  space;  the  proportions  are  therefore  changed  so 
as  to  give  the  ordinary  shape  shown  in  Fig.  305,  and  for  a  given 

rating  it  will  be  found  that  the  ratio  ~y  is  about  four  times  as 

large  for  the  transformer  in  Fig.  305  as  it  is  for  that  in  Figs.  303 
or  304;  that  is,  the  shell-type  transformer  has  generally  twice 
the  flux  and  half  the  number  of  turns  that  the  core-type  trans- 
former has  for  the  same  rating.  The  distance  a  is  generally 
about  QXb  to  give  a  reasonable  shape  of  core. 


FIG.  305. — Shell-type  transformer. 

336.  Procedure  in  the  Design  of  Core -type  Transformers. 
1      

The  volts  per  turn  =  ^V  watts   for  power  transformers 

1 

=  orA/watts   for  distributing  transformers. 

oU 

The  number  of  coils  is  chosen  so  as  to  keep  the  voltage  per  coil  less 
than  5000,  but  there  should  not  be  less  than  two  high-voltage 
and  two  low-voltage  coils;  the  number  of  turns  per  coil  is  equal  to 

_^ terminal  voltage 

volts  per  turn  X  number  of  coils 

The  depth  of  the  coil  measured  from  the  nearest  oil  duct  should 
not  be  greater  than  1.0  in.,  except  in  the  case  of  small  distributing 


PROCEDURE  IN  DESIGN  479 

transformers  insulated  as  shown  in  Fig.  288  which  have  no  oil 
duct  between  the  low  voltage  winding  and  the  core.  In  such  a 
case  the  depth  from  the  core  to  the  oil  may  be  2  in.,  the  reason 
being  that  the  heat  in  the  inner  layers  of  the  winding  is  con- 
ducted through  the  insulation  into  the  core  and  dissipated  by 
the  core  surface. 

The  section  of  the  wire  in  circular  mils  is  found  from  formula  67, 
page  475,  namely, 

cir.  mils  per  amp.  =  1350\/(1  —  k)2x2X  where 
X=  the  greatest  depth  from  the  inside  of  the  winding  to  the 

nearest  oil  or  core  surface, 
(1  —  k) 2  =  per  cent,  copper  in  the  vertical  layers  of  the  winding  X 

that  in  the  horizontal  layers 

and  the  area  of  the  wire  is  the  product  of  the  full-load  current 
in  the  winding  and  the  circular  mils  per  ampere.  The  section  of 
wire  should  be  chosen  so  that  it  is  not  thicker  than  0.125  in.,  and 
the  wire  should  be  wound  flat  as  shown  at  A,  Fig.  292. 

The  number  of  layers  in  the  winding  is  the  same  as  the  number 
of  wires  in  the  assumed  depth  of  the  coil;  the  number  of  conduc- 
tors per  layer  is  the  total  number  of  turns  per  coil  divided  by  the 
number  of  layers,  and  the  height  of  the  winding  is  the  number  of 
turns  per  layer  multiplied  by  the  width  of  the  wire  in  the  direc- 
tion parallel  to  the  limbs  of  the  core. 

The  flux  in  the  core  is  found  from  formula  62,  page  439;  namely, 
E  =  4.44  X  turns  X  flux  X  frequency  XlO~8 

flux  in  core       ,  ,  ,, 

and  the  core  area  =  -     —5 rr— ,  where  the  value  of  the  core 

core  density 

density  is  taken  for  a  first  approximation, 

=  65,000  lines  per  square  inch  60-cycle  distributing  transformers 
=  75,000  lines  per  square  inch  25-cycle  distributing  transformers 
=  90,000  lines  per  square  inch  60-cycle  power  transformers 
=  80,000  lines  per  square  inch  25-cycle  power  transformers 
alloyed  iron  being  used  for  60-cycle  transformers,  to  keep  down 
the  loss  in  the  distributing  transformer  so  as  to  have  a  high  all- 
day  efficiency,  and  to  keep  down  the  heating  in  the  power  trans- 
formers. Ordinary  iron  is  used  for  25-cycle  transformers,  be- 
cause, due  to  the  low  frequency,  the  loss  is  generally  small,  while 
the  densities  have  to  be  kept  low  in  order  that  the  magnetizing 
current  will  not  be  too  large  a  per  cent,  of  the  full-load  current. 
The  core  and  windings  are  drawn  in  to  scale;  the  losses, 
magnetizing  current,  resistance  and  reactance  drops  are  deter- 


480  ELECTRICAL  MACHINE  DESIGN 

mined,  and  the  size  of  the  tank  is  fixed.  If  the  transformer  as 
designed  does  not  meet  the  guarantees  then  certain  changes 
must  be  made. 

If  the  core  loss  is  too  high,  either  the  core  density  must'  be 
reduced,  which  will  increase  the  size  of  the  transformer,  or  the 
total  flux  must  be  reduced,  which  will  require  an  increase  in  the 
number  of  turns  for  the  same  voltage,  and,  therefore,  an  increase 
in  the  copper  loss. 

The  resistance  and  the  reactance  drops  may  both  be  reduced 
by  a  reduction  in  the  number  of  turns,  because  the  resistance  is 
directly  proportional  to  the  number  of  turns,  while  the  reactance 
is  proportional  to  the  square  of  the  number  of  turns. 

Example. — Design  and  determine  the  characteristics  of  a  15- 
k.  v.  a.,  2200-  to  220-volt,  60-cycle  distributing  transformer. 

Design  of  the  High-voltage  Winding 

Volts  per  turn  =1.52 

Total  number  of  turns  =  1440 

Coils  =  2;  one  on  each  leg 

Turns  per  coil  =  720 

Total  depth  of  winding  =2.0  in.,  assumed 


Cir.  mils  per  ampere  =  1350  X  \/2  X  °-9  X  0.8 

=  1620 

Full-load  current  =6.8  amp. 

Section  of  wire  =11,000  cir.  mils; 

use  no.  10  square  B.  &  S. 
=  0.1019  in.  X0.1019  in. 
which  has  a  section  of  13,000  cir.  mils, 
not  allowing  for  rounding  of  the  corners 
Insulation  =0.01  in.  double  cotton-covering, 

0.014  in.  fullerboard  between  layers 

/I      7N  0.1019         -  ' 

(1-fc)    vertical    =  o7Tl9 


Number  of  layers 


(1-&)  horizontal  = 


0.1019  +  0.01  +  0.014 

=  8 

Turns  per  layer  =90 

Height  of  winding  =  90  X  (0.1019  +  0.01) 

=  10  in. 
Height  of  opening  =11.75  in. ;  see  Fig.  288 

Design  of  the  Low-voltage  Winding 

Total  number  of  turns  =  1440  X  ratio  of  transformation 

=  144 


PROCEDURE  IN  DESIGN  481 

Turns  per  coil  =  72 

Circular  mils  per  amperes  =1620;  the  same  as  for  the  high- voltage 

coil 

Section  of  wire  =110,000  circular  mils 

=  0.087  sq.  in. 
=  0.11  in.  X0.8  in.;  this  will  be  difficult  to 

wind  on  a  small  transformer  because  of 

its  width,  therefore,  change  the  winding 

as  follows: 
Turns  per  coil  =  72 ;  number  of  coils  =  4   connected  two   in  parallel ;  size  of 

wire  =  0.11  in.  X  0.4  in. 
Insulation  =0.015  in.  cotton  covering 

0.014  in.  fullerboard  between  layers 

winding  height 
Turns  per  layer  =  — 

width  of  wire 

-iM 
~0.415 
=  24 

72 
Number  of  layers  per  coil  =  — 

=  3 

Number  of  layers  per  leg  =6,  because  there  are  two  coils  per  leg 

Depth  of  winding  =  (0.11  in.  +0.015  in.  +0.014  in.)  6 

=  0.83  in. 
Thickness  of  insulation  between  the  high-  and  low- voltage  coils  =  0.12  in. 

Design  of  Core 

Flux  =5.72X105 

Core  density,  assumed  =65,000  lines  per  square  inch 

Necessary  core  section  =8.8  sq.  in 

Actual  section  adopted  =2.5X4  and  stacking  factor  =0.9 

Width  of  opening  =4.5  in.,  to  allow  a  little  clearance  between 

coils  on  different  legs ;  see  Fig.  288. 

Calculation  of  the  Losses  and  the  Magnetizing  Current 

Mean  turn  of  low- voltage  coil         =  16.6  in. 

144X16.6 
Resistance  of  secondary  winding    =  — 

2X0.11X0.4X1.27X106 

=  0.021  ohms 
Mean  turn  of  high- voltage  coil         =24  in. 

1440X24 

Resistance  of  primary  winding        = 

13000 

=  2.6  ohms 

Loss  in  primary  winding  =2.6X6.82 

=  120  watts 
31 


482  ELECTRICAL  MACHINE  DESIGN 

Loss  in  secondary  winding  =0.021  X682 

=  97  watts 

Weight  of  core  =1101b. 

Actual  core  density  =63,500  lines  per  square  inch 

Core  loss  in  watts  (alloyed  iron)     =110x0.9;  from  Fig.  275,  page  442. 

=  99  watts 
Volt  amperes  excitation  =110X5 

=  550 
Per  cent,  exciting  current  =3.3 

Calculation  of  the  Regulation 

Equivalent  primary  reactance  =  2  TT/X  3.  2  T^X—.  —  '  (—  +  —  +s)  10~8X2 

L     \3      3        / 

where  /     =60 
T,    =720 

16.6  +  24 


..         . 
Xeq  of  primary  =  27rX60X3.2x7202X  -    -  -+0.12    X10~8X2 


=  20.3  in. 
L     =10  in. 
dl     =1.0  in. 
d2     =0.83  in. 
S      =0.12  in. 
coils  =  2 

20.4/1.0  +  0.83 
(- 

10   \         3 

=  18.6  ohms 
The  reactance  drop  referred  to  the  primary  =18.6X6.8 

=  126  volts 

=  5.8  per  cent. 
The  primary  resistance  drop  =2.6x6.8 

=  17.6  volts 
The  secondary  resistance  drop  =0.021  X  68 

=  1.43  volts 

The  resistance  drop  referred  to  the  primary  =  17.6  +  1.  43  X  — 

=  31.9  volts 
=  1.44  per  cent. 
Design  of  the  Tank 
The  total  losses  at  full-load  are: 

Iron  loss,  99  watts 

Primary  copper  loss,  120  watts 

Secondary  copper  loss,  97  watts 

Total  loss,  316  watts 

The  watts  per  square  inch  for  35  deg.  cent,  rise  of  the  oil  =  0.225,  therefore 
the  tank  surface  in  contact  with  the  oil 
_  316 
~  0.225 
=  1400  sq.  in. 


PROCEDURE  IN  DESIGN  483 

337.  Procedure  in  the  Design  of  a  Shell  -type  Transformer.— 

The  work  is  carried  out  in  exactly  the  same  way  as  for  a  core-type 
transformer  except  that  the  width  of  the  coil  is  seldom  made 
greater  than  about  0.5  in.,  so  as  to  provide  ample  radiating  sur- 
face and  allow  the  use  of  comparatively  high  copper  densities. 

The  number  of  coils  is  again  chosen  so  as  to  keep  the  voltage 
per  coil  less  than  5000;  still  further  subdivision  of  the  winding 
may  be  required  in  some  cases  to  reduce  the  reactance. 

Example.  —  Design  a  1500  -  k.v.a.,  63,500-  to  13,200-volts,  25- 
cycle  power  transformer  for  operation  in  a  three-phase  bank  on 
a  110,000  volt  line. 

Dssign  of  the  High-voltage  Winding 

Volts  per  turn  =  49 

Total  number  of  turns        =  1300 

Coils  =12 

Turns  per  coil  =108  average;  use  10  coils  with  113  turns  and  2 

end  coils  with  85  turns 
Width  of  coil,  assumed       =0.4  in. 

Because  of  the  high  voltage  the  distance  x,  Fig.  291,  will  be  large,  and  there 
will  be  little  iron  saved  by  making  the  strip  wider  than  0.4  in.  with  the  idea 
of  keeping  the  distance  x  small. 
Circular  mils  per  ampere    =  1260  X  \/0.4X0.6 

where  (1-&)2  is  assumed  to  be  =  0.6 
=  615. 
Section  of  wire  =14,500  circular  mils 

=  0.0285X0.4  in. 

Insulation  =0.015  in.  cotton  covering 

0.014  in.  fullerboard 
,.     0.0285 


Under  ordinary  circumstances  the  calculation  for  the  size  of  conductor 
would  be  repeated  using  the  correct  value  for  (l-k)  to  find  the  value  of  the 
circular  mils  per  ampere.  In  a  very  high  voltage  transformer,  however,  the 
amount  of  copper  is  small  compared  with  the  amount  of  iron  and  insulation, 
so  that  it  is  not  advisable  to  run  the  chance  of  high  temperature  rise  for  a 
small  gain  in  the  amount  of  copper  used.  The  conductor  chosen  for  this 
transformer  is  therefore  0.03X0.4  in. 

Height  of  winding  =  turns  X  thickness  of  insulated  wire 

=  113  X  (0.03  +  0.015  +  0.014) 

=  6.7  in. 

=  7  in.  to  allow  for  bulging 
Space     between     winding 

and  core  =4.5  in.,  from  Fig.  290. 

Width  of  opening  =  7  +  (2  X  4  .  5) 

=  16  in. 


484 


ELECTRICAL  MACHINE  DESIGN 


The  arrangement  of  the  winding  must  now  be  decided  on  and  several 
possible  methods  are  shown  in  Fig.  306.  A  would  give  a  very  long  core  and 
take  up  a  large  floor  space,  it  would  also  have  a  large  core  loss  and  magnetiz- 
ing current  because  of  the  large  amount  of  iron  in  the  magnetic  circuit,  but 
of  the  three  shown  it  would  have  the  lowest  reactance. 

B  would  have  a  lower  magnetizing  current  and  a  lower  core  loss  than  A, 
it  would  also  be  considerably  cheaper,  but  would  have  a  larger  reactance. 

C  will  have  values  of  core  loss,  magnetizing  current  and  reactance  be- 
tween these  of  A  and  B,  and  the  design  will  be  completed  for  this  arrange- 
ment to  find  its  characteristics. 


FIG.  306. — Arrangement  of  coils  in  a  110,000-volt  shell-type  transformer. 


Design  of  the  Low-voltage  Winding 


Total  number  of  turns 

Coils 

Turns  per  coil 

Width  of  copper  assumed 

Circular  mils  per  ampere 


Section  of  wire 


=  270 
=  6 
=  45 
=  0.4  in. 

=  1260  X\/0-4X  0.9 

where  (1-&)2  is  assumed  to  be  =  0.9 
=  755 

=  86,000  circular  mills 
=  0.17  in.  X  0.4  in. 

use  2  X  (0.085  in.  X  0.4  in.)   with  a  strip   of 

fuller-board  between 


PROCEDURE  IN  DESIGN  485 

Insulation  =0.007  fullerboard  between  wires 

0.024  half  lap  cotton  tape 
0.014  fullerboard  between  layers 
Thickness  of  insulated  strip  =0.215  in. 
Height  of  winding  =0.215X45 

=  9.7  in. 

=  10.2  in.  to  allow  for  bulging. 

This  allows  ample  clearance  between  the  winding  and  the  core,  in  fact  the 
winding  could  be  made  narrower  and  higher  because  0.75  in.  would  be 
ample  spacing  for  13,200  volts,  but  it  is  advisable  to  use  the  larger  spacing, 
where  it  is  available  without  any  sacrifice  of  space  or  material. 

The  coils  with  the  insulation  are  now  drawn  to  scale  as  shown  in  Fig.  291, 
and  the  length  of  the  opening  determined;  this  value  is  43  in. 

Design  of  the  Core 

Flux  =44X10° 

Core  density,  assumed  =  80,000  lines  per  square  inch 

Necessary  core  section  =550  sq.  in. 

Actual  section  adopted  =  14  X 43. 5  in. 

Calculation  of  the  Losses  and  the  Magnetizing  Current 

Mean  turn  of  the  low- voltage  winding  =  170  in. 

..,     ,  .    ,.  6X45X170 

Resistance  of  the  low-voltage  winding 


0.17  X  0.4  X  1.27  X106 
=  0.53  ohms 
Mean  turn  of  high- voltage  winding  =  190  in. 

...  ,        u  .    ,.  1300X190 

Resistance  of  high- voltage  winding  =  0.03  x  0.4  X  1.27  X  106 

=  16.2  ohms 
Loss  in  the  high- voltage  winding  =  16.2  X  23.62 

=  9000  watts 
Loss  in  the  low- voltage  winding  =0.53  X 1142 

=  6900  watts 

Weight  of  core  =22,000  Ib. 

Core  loss  in  watts  (ordinary  iron)  =22000X0.9;  from  Fig.  275. 

=  20,000  watts 

Total  loss  at  full-load  =  35,900  watts 

Efficiency  =97.7  per  cent. 

Volt  amperes  excitation  =  22000  X  5.4 

=  119,000 

=  8  per  cent. 

The  equivalent  primary  reactance   =  2;r/X  3. 2  X  ZV  ^  (^  +  ^  +  S  \  X  10 

X  coil  groups 
where          MT.  =180  in. 
L  =  16  in. 

d,  =  1.3  in.     See  Figs.  279  and  291. 
d2  =  0.4in. 
5  =  4.5  in. 


486  ELECTRICAL  MACHINE  DESIGN 

coil  groups  =6;  diagram  C,  Fig.  306 
Equivalent  primary  reactance  =2^X25x3.2x2162X^  (~  +  4:.5\  10~8X6 

=  80  ohms 

The  reactance  drop  referred  to  the  primary   =80X23.6 

=  1900  volts 
=  3.0  per  cent. 

The  primary  resistance  drop  =380 

The  secondary  resistance  drop  referred  to 

the  primary  =  60  X  ^j  =  290 

The  resistance  drop  referred  to  the  primary  =  670 

=  1.05  per  cent. 

The  tank  is  made  round  in  section  and  clears  the  core  by  2  in.  at  the  corners. 

The  total  loss  =35,900  watts 

The  water-pipe  surface  required  =35,000  sq.  in. 

=  750  ft.  of  1  1/4-in.  pipe. 


CHAPTER  XL VII 
SPECIAL  PROBLEMS  IN  TRANSFORMER  DESIGN 

338.  Comparison  between  Core-  and  Shell-type  Transformers.— 

Figs.  303  and  305  show  the  two  types  built  for  the  same  output 
and  drawn  to  the  same  scale.  It  was  shown  in  Art.  335,  page  476, 
that,  due  to  the  difference  in  the  construction,  the  volts  per  turn 
has  twice  the  value  for  shell-type  that  it  has  for  core-type  trans- 
formers, in  fact 

volts   per  t urn  =  -— ^/  watts  for  shell-type    power  transformers 
Zo 

=  —  \/watts  for  core-type  power  transformers 
ol) 

so  that  the  number  of  turns  for  a  given  voltage  is  the  smaller  for 
transformers  of  the  shell  type. 

The  essential  differences  between  the  two  types  are:  For  the- 
same  voltage  and  output  the  shell  type  has  half  as  many  turns 
as  the  core  type,  it  has  also  the  longer  mean  turn  of  coil,  but 
the  smaller  total  amount  of  copper. 

The  shell  type,  since  it  has  half  as  many  turns,  must  have 
twice  the  flux  of  the  core  type  and,  because  of  that,  must  have 
twice  the  core  section;  but  the  mean  length  of  magnetic  path  is 
shorter  and  the  total  weight  of  iron  only  slightly  greater. 

Since,  as  shown  on  page  443,  the  magnetizing  current  and  the 
iron  loss  are  proportional  to  the  weight  of  the  core  for  a  given 
frequency  and  density,  transformers  of  the  core  type  can  more 
readily  be  designed  for  small  iron  loss  and  small  exciting  current 
than  can  those  of  the  shell  type,  and  for  that  reason  are  generally 
used  for  distributing  transformers,  since  these  are  built  with  a 
small  iron  loss  so  as  to  have  a  high  all-day  efficiency.  It  must, 
of  course,  be  understood  that  by  changing  the  proportions  some- 
what, shell-type  transformers  can  also  be  built  suitable  for  dis- 
tributing service,  but  the  fact  that  the  core  type  is  the  one  gener- 
ally used  would  indicate  that  for  such  service  it  is  the  cheaper 
to  construct. 

For  very  high-voltage  service  the  losses  are  not  of  so  much 

487 


488 


ELECTRICAL  MACHINE  DESIGN 


importance  as  reliability  in  operation.  Fig.  307  shows  the  relative 
proportions  of  a  high-voltage  core  and  of  a  high  voltage  shell  type 
transformer;  the  coils  of  such  transformers  are  not  easily  braced 
and  supported  if  the  core-type  of  construction  is  used,  and  the 
forces  due  to  short-circuits  are  more  liable  to  destroy  the  winding 
than  in  the  case  of  shell-type  transformers,  in  which  the  coils  are 
braced  in  such  a  way  that  these  forces  cannot  bend  them  out 
of  shape. 


FIG.  307. — High  voltage  core,  and  shell-type  transformers. 

terminal  voltage 


The  current  on  a  dead  short-circuit  = 


impedence  of  winding 
and  may  reach,  in  power  transformers,  a  value  of  50  times  full- 
load  current.  In  the  case  of  an  instantaneous  short-circuit  the 
current  may  reach  still  greater  values  depending,  as  shown  in 
Art.  209,  page  284,  on  the  point  of  the  voltage  wave  at  which  the 
short-circuit  takes  place.  Since  the  forces  tending  to  separate  the 
high-  and  low-voltage  windings,  and  to  pull  together  the  turns  of 
windings  of  the  same  coil,  are  proportional  to  the  square  of  the 


SPECIAL  PROBLEMS  IN  TRANSFORMER  DESIGN    489 

current,  they  may  reach  very  large  values  on  short-circuit  and 
may  destroy  the  winding.  Of  the  two  types  of  transformer,  the 
shell-type  is  the  better  able  to  resist  such  forces. 

The  winding  of  a  transformer  is  divided  up  into  a  number  of 
coils  in  series,  and  the  voltage  per  coil  should  not  exceed  about 
5000  volts.  It  will  generally  be  found  that  the  distance  X,  over 
which  this  voltage  is  acting,  is  less  in  the  core-  than  in  the  shell- 
type  transformer. 

The  reactance  of  a  transformer  depends  on  the  square  of  the 
number  of  turns,  and  on  the  way  in  which  the  winding  is  sub- 
divided. Due  to  the  large  space  required  between  the  high-  and 
low-voltage  coils  it  is  not  practicable  to  subdivide  the  winding 
of  a  core-type  transformer  more  than  is  shown  in  Fig.  307,  while 
the  shell  type  winding  can  be  well  subdivided  before  the  length 
Y  is  greater  than  that  required  for  a  cylindrical  tank.  Because 
of  this,  and  also  because  it  has  the  smaller  total  number  of  turns, 
the  reactance  of  a  shell-type  transformer  can  readily  be  kept 
within  reasonable  limits  while  that  of  a  core  type  cannot,  in- 
deed, it  is  principally  because  certain  regulation  guarantees 
are  demanded  that  the  shell  type  has  to  be  used,  although  it 
is  doubtful  if  good  regulation  and  the  consequent  large  short- 
circuit  current  is  as  desirable  for  power  transformers  as  poorer 
regulation  and  a  smaller  current  on  short-circuit. 

So  far  as  the  coils  themselves  are  concerned  the  shell  type  of 
transformer,  in  large  sizes,  has  the  advantage  that  strip  copper 
wound  in  one  turn  per  layer  may  be  used;  this  gives  a  stiff  coil 
and  one  not  liable  to  break  down. 

For  outputs  up  to  500  k.  v.a.  at  110,000  volts  the  core  type 
will  probably  be  the  cheaper,  and  for  outputs  greater  than  1000 
k.v.a.  the  shell  type  must  be  used  to  keep  the  reactance  drop 
within  reasonable  limits;  between  these  two  outputs  the  type  to 
be  used  depends  largely  on  the  previous  experience  of  the  designer. 

The  core-type  transformer  has  the  great  advantage  that  it 
can  be  easily  repaired,  especially  if  built  with  butt  joints  so 
that  the  top  limb  may  be  removed  and  the  windings  and  insula- 
tion lifted  off. 

339.  Three-phase  Transformers. — Diagram  A,  Fig.  308,  shows 
a  single-phase  transformer  with  all  the  windings  gathered  to- 
gether on  one  leg,  and  diagram  B  shows  three  such  transformers 
with  the  idle  legs  gathered  together  to  form  a  resultant  magnetic 
return  path.  The  flux  in  that  return  path  is  the  sum  of  three 


490 


ELECTRICAL  MACHINE  DESIGN 


B 


D 


E  F 

FIG.  308. — Development  of  the  three-phase  core-type  transformer. 


SPECIAL  PROBLEMS  IN  TRANSFORMER  DESIGN    491 

fluxes  which  are  120  electrical  degrees  out  of  phase  with  one 
another  and  is  therefore  zero,  the  center  path  may  therefore  be 
dispensed  with. 

In  diagram  B  the  flux  in  a  yoke  is  the  same  as  that  in  a  core, 
the  yoke  and  core  have  therefore  the  same  area.  If  the  three  cores 
are  connected  together  at  the  top  and  bottom  as  shown  in  diagram 
C,  then  the  three  yokes  form  a  delta  connection,  and,  as  shown  by 
the  vector  diagram  D,  the  flux  in  the  yoke  is  less  than  that  in  the 

core  in  the  ratio  —•=*  and  the  yoke  section  may  be  less  than 
v  3 

that  of  the  core.  The  bank  of  transformers  may  be  still  further 
simplified  by  operating  it  with  a  V  or  open  delta-connected 
magnetic  circuit  as  shown  in  diagram  E,  and  this  latter  trans- 
former, when  developed  on  to  a  plane  as  shown  in  diagram  F, 
gives  the  three-phase  core  type  that  is  generally  used.  There  is 


FIG.  309. — Three  phase  shell-type  transformer. 

a  considerable  reduction  in  material  between  three  transformers, 
such  as  that  in  diagram  A,  and  the  single  transformer  in  diagram 
F,  so  that  the  three-phase  transformer  is  cheaper,  has  less  mate- 
rial, greater  efficiency,  and  takes  up  less  room  than  three  single- 
phase  transformers  of  the  same  total  output. 

So  far  as  the  design  is  concerned  there  is  no  new  problem; 
each  leg  is  treated  as  if  it  belonged  to  a  separate  single-phase 
transformer. 

Diagram  A,  Fig.  309,  shows  a  single-phase  shell-type  trans- 
former, and  diagram  B  shows  three  such  transformers  set  one 
above  the  other  to  form  a  three-phase  bank.  If  the  three  coils 


492 


ELECTRICAL  MACHINE  DESIGN 


were  all  wound  and  connected  in  the  same  direction,  as  in  the 
case  of  the  three-phase  core-type  transformer,  then  the  flux  in 
the  core  at  M  would  be  produced  by  three  m.m.fs.,  120 
degrees  out  of  phase  with  one  another,  and  would  be  zero,  because 
at  any  instant  the  m.m.f.  of  one  phase  would  be  equal  and  oppo- 
site to  the  sum  of  the  m.m.fs.  of  the  other  two  phases.i  The  center 
coil  is  connected  backward  and  the  direction  of  the  flux  in  the 


Section  of  the  iron  core. 


FIG.  310. — Three-phase  shell- type  transformer. 

cores  and  cross  pieces  at  one  instant  is  shown  by  the  arrows. 
The  total  flux  in  one  of  the  cross  pieces,  say  A,  is  the  sum  of  the 
fluxes  in  cores  1  and  2,  and  the  value  may  be  found  from  dia 
gram  C. 

A  very  economical  type  of  three-phase  transformer  is  shown 
in  Fig.  310;  it  is  almost  circular  in  section  and  may  be  used  in  a 
cylindrical  tank. 


SPECIAL  PROBLEMS  IN  TRANSFORMER  DESIGN    493 

340.  Operation  of  a  Transformer  at  Different  Frequencies.  — 
The  e.m.f.          =E 

-4.44 


=  4.44!T£mAc/10-8 

=  a  const.  X-BmX/for  a  given  transformer; 
the  iron  losses  =  hysteresis  loss  +  eddy-current  loss 

=  KBm1'*+KeBm22  for  a     iven  transfor 


*f+KeBm2f2  for  a  given  transformer 

E1'9 

=  a  const.  X-76  +  a  const.  X  E2 


so  that,  for  a  given  voltage,  as  the  frequency  increases  the 
hysteresis  loss  decreases,  while  the  eddy-current  loss  remains 
constant.  A  standard  transformer,  designed  for  a  definite 
frequency,  may  operate  at  frequencies  which  are  considerably 
higher  or  lower  than  that  for  which  the  transformer  was  designed; 
if  the  transformer  is  designed  so  that  at  normal  frequency  and  full- 
load  the  copper  and  iron  losses  are  equal  and  the  efficiency  a 
maximum,  then  at  lower  frequencies  the  iron  loss  will  be  larger 
than  the  copper  loss,  and  at  higher  frequencies  the  copper  loss 
will  be  the  greater. 

In  order  that  a  low-frequency  transformer  may  have  approxi- 
mately the  same  core  loss  and  copper  loss  at  full-load,  the  section 
of  the  iron  in  the  core  must  be  increased  over  that  required  for  a 
transformer  of  the  same  rating  but  of  higher  frequency,  in  order 
to  lower  the  densites  and  reduce  the  core  loss,  so  that,  for  the 
same  rating  and  efficiency,  the  lower  the  frequency,  the  larger 
the  amount  of  iron,  and  the  heavier  the  transformer. 


CHAPTER  XLVIII 
SPECIFICATIONS 

341.  The  following  specification  is  intended  to  cover  a  line 
of  transformers  for  lighting  and  power  service  and  for  sizes  up  to 
50  k.v.a. 

STANDARD  SPECIFICATION  FOR  OIL-IMMERSED,  SELF-COOLED 

TRANSFORMERS 

Rating. — Rated  capacity  in  kilovolt  amperes 1  to  50 

Normal  high  voltage 2200  and  1100 

Normal  low  voltage  at  no-load 220  and  110 

Phases 1 

Frequency  in  cycles  per  second 60 

Construction. — The  transformers  are  for  combined  lighting 
and  power  service.  The  windings  shall  be  so  arranged  that  with 
either  2200  or  1100  volts  on  the  primary  side  the  secondary  volt- 
age may  be  either  110  or  220;  taps  must  also  be  supplied  so  that 
if  desired  the  secondary  voltage  may  be  raised  5  or  10  per  cent, 
with  normal  applied  high  voltage.  The  tanks  must  be  of  cast 
iron  or  sheet  iron  of  approved  shape  and  construction,  must  be  im- 
pervious to  oil  and  water,  and  have  covers  supplied  with  gaskets. 
Eye  bolts  or  hooks  must  be  supplied  for  the  lifting  of  the  tank 
with  the  transformer  and  oil.  With  transformers  larger  than 
5  k.v.a.  output,  oil  plugs  must  be  supplied  at  the  bottom  of  the 
tank  for  the  removal  of  the  oil.  Four  secondary  leads  and  two 
primary  leads  shall  be  brought  out  of  the  tank  through  porcelain 
bushings  properly  cemented  in.  The  transformer  itself  shall  be 
properly  anchored  in  the  tank  to  prevent  movement. 

Core. — This  shall  be  of  non-ageing  steel  assembled  tightly  so  as 
to  prevent  buzzing  during  operation. 

Windings. — The  high-  and  low-voltage  coils  must  be  insulated 
from  one  another  by  a  shield  of  ample  dielectric  strength.  The 
coils,  when  wound,  shall  be  baked  in  a  vacuum  and  then  impreg- 
nated with  a  compound  which  is  waterproof  and  is  not  acted  on 
by  transformer  oil  over  the  range  of  temperature  through  which 
the  transformer  may  have  to  operate. 

494 


SPECIFIC  A  TIONS  495 

Oil. — The  oil  supplied  with  the  transformer  shall  be  a  mineral 
oil  suitable  for  transformer  insulation,  and  must  be  free  from 
moisture,  acid,  alkali,  sulphur  or  other  materials  which  might 
impair  the  insulation  of  the  transformer.  It  should  have  a  flash- 
point higher  than  139  deg.  cent,  and  a  dielectric  strength  greater 
than  40,000  volts  when  tested  between  half  inch  spheres  spaced 
0.2  in.  apart.  Sufficient  oil  must  be  contained  in  the  tank  to 
submerge  the  windings  and  the  core  at  all  temperatures  from  0 
to  80  deg.  cent. 

Cut  Outs. — Two  plug  cut  outs  shall  be  supplied  for  the  high- 
voltage  side  of  the  transformer  for  operation  up  to  2500  volts. 
Workmanship  and  Finish. — The  workmanship  shall  be  first 
class  and  the  materials  used  in  the  construction  of  the  highest 
grade.  The  tank  shall  be  thoroughly  painted  with  a  black 
waterproof  paint. 

General. — Bidders  shall  furnish  cuts  with  descriptive  matter 
from  which  a  clear  idea  of  the  construction  may  be  obtained. 
They  shall  also  state  the  following: 
Net  weight  of  transformer. 
Net  weight  of  case. 
Net  weight  of  oil. 
Shipping  weight. 
Dimensions  of  the  tank. 
Core  loss. 

Copper  loss  at  full-load. 

Regulation  at  100  per  cent,  and  at  80  per  cent,  power  factor. 
Exciting  current  at  normal  voltage  and  at  20  per  cent,  over  normal 

voltage. 

The  core  loss  shall  be  taken  as  the  electrical  input  determined 
by  wattmeter  readings,  the  transformer  operating  at  no-load,  on 
normal  voltage  and  frequency,  and  with  a  sine  wave  of  applied 
e.m.f. 

The  copper  loss  shall  be  taken  as  the  electrical  input  deter- 
mined by  wattmeter  readings,  the  transformer  being  short- 
circuited  and  full-load  current  flowing  in  the  high-voltage  coils; 
measurements  to  be  made  on  the  high-voltage  side. 

The  regulation  shall  be  calculated  by  the  use  of  the  following 
formulae;  the  per  cent,  regulation 

=  100 t"~(~r)      a^  100  per  cent,  power  factor 

L  E      2\  E  j  j 

/0.8/E+0.6/Z\ 
=  100  (  -       ~~E^      ~  J  at  80  Per  cent-  Power 


496  ELECTRICAL  MACHINE  DESIGN 

where  E  is  the  normal  secondary  voltage  at  no-load 

I  is  the  full-load  secondary  current 
IR  is  the  resistance  drop  in  terms  of  the  secondary 
IX  is  the  reactance  drop  'in  terms  of  the  secondary. 
These  two  latter  values  are  to  be  found  by  short-circuiting  the 
secondary  winding  and  measuring  the  applied  voltage  and  the 
watts  input  required  to  send  full-load  current  through  the  primary 
winding. 

watts  input 

secondary  full-load  current 
IZ   =  the  impedence  drop  in  terms  of  the  secondary 

220 

=  the  short-circuit  voltage  X  7^™ 


IX  =  V(IZ)2-(IRY2 

Temperature.  —  The  transformer  shall  carry  the  rated  capacity 
at  normal  voltage  and  frequency  and  with  a  sine  wave  of  applied 
e.m.f  .  for  24  hours,  with  a  temperature  rise  that  shall  not  exceed 
45  deg.  cent,  by  resistance  or  thermometer  on  any  part  of  the 
windings,  core  or  oil,  and,  immediately  after  the  full-load  run, 
shall  carry  25  per  cent,  overload  at  the  same  voltage  and  fre- 
quency for  two  hours,  with  a  temperature  rise  that  shall  not  exceed 
55  deg.  cent,  by  resistance  or  thermometer  on  any  part.  The 
temperature  rise  shall  be  referred  to  a  room  temperature  of 
25.  deg.  cent. 

Insulation.  —  The  transformers  shall  withstand  a  puncture  test 
of  10,000  volts  for  one  minute  between  the  high-voltage  winding 
and  the  core,  tank,  and  low-voltage  winding;  also  a  puncture 
test  of  2500  volts  for  one  minute  between  the  low-  voltage  winding 
and  the  core  and  tank. 

The  transformer  shall  operate  without  trouble  for  five  minutes 
at  double  normal  voltage  and  no-load;  the  frequency  may  be  in- 
creased during  this  test  if  desired. 

These  insulation  tests  shall  be  made  -immediately  after  the 
heat  run. 

342.  Effect  of  Voltage  on  the  Characteristics.  —  The  effect  of 
high  voltage  in  a  transformer  is  that  large  spacings  are  required 
between  the  high-  and  low-voltage  coils  and  also  between  the 
high-voltage  coils  and  the  core,  so  that  the  higher  the  voltage  the 
longer  the  magnetic  path  and  also  the  mean  turn  of  the  coils. 
Because  of  the  large  spacings,  the  reactance  of  high-voltage 
transformers  is  greater  than  of  those  of  lower  voltage,  and  the 


SPECIFICATIONS 


497 


i-l   O   O   O        OOOO5        Oi   l>   l>   O 
CO   CO   CO   CO        CO   CO   CO   <N        <N    <N    <N    <N 


1O    CO    CO 


CO    *O    CO        C^i— IO500        t>COiOTf        CO 


CO    O    Ci    TJH        O5    CO    00 


CO   00   O   i—  I 


00000000 


OOOii-i(M 


000000 


OOOO 

o^  o^ 


OOOOOOOO 


lO  CO  »O  i-l   CO  00 
1C  CO  l>  Oi   (N  IO 


»O  i-H   CO  00  (N 
(N  »O  TH 

i-l  i-l  (N 


»-H(M(M(N        COCOCO^H 


r^        1C   CO   (N    <M 

(M          TtH    CO    O    TtH 

r-l        i-H    i-l    (M    (N 


O^O^OO        OOO»O        >O>OOO 
i— I    -^    CO    (M        i— I    O    »O    (N        C^llNiOTfri 

<N(N(NCO          TfHlOCOCJ          Or-HlOOO 


OiO^OO        OOOiO        O^O»OO        OOOO 

rHrHi-l<N          (NCOCOCO          TjHCOt^rH          (M<NOCO 


lOOOO        OOOO        OOOO 
COl>«l>OS        C^-^I>T}H        CDCOCDO 

i— IrHrHCO          COCO&OCO 


1>OOO<N 


i-l    I-H    (N        (N    CO 


32 


498  ELECTRICAL  MACHINE  DESIGN 

regulation  is  poorer.  Because  of  the  longer  mean  turn  of  the 
coils  and  of  the  magnetic  circuit  the  losses  are  greater  and  the 
efficiency  poorer  than  for  a  transformer  of  the  same  output  but  of 
lower  voltage. 

The  table  on  page  497  gives  the  characteristics  of  a  line  of 
60-cycle  distributing  transformers. 


CHAPTER  XLIX 
MECHANICAL  DESIGN 

343.  A  complete  discussion  of  the  mechanical  design  of  electri- 
cal machinery  is  beyond  the  scope  of  this  work,  but  there  are 
several  points  which  the  student  is  liable  to  overlook  unless  his 
attention  is  drawn  to  them. 

The  fundamental  principle  in  the  design  of  revolving  machinery 
is  that  the  frame  shall  be  as  heavy  as  possible,  the  revolving 
part  as  light  as  possible,  and  the  shaft  as  stiff  as  possible. 

The  yokes,  housings,  spiders  and  bases  should  be  designed  so 
that  the  work  in  moulding  them  shall  be  a  minimum,  and  the 
smaller  parts,  when  used  in  large  quantities,  should  be  designed 
for  machine  moulding. 


FIG.  311. — Alternator  yoke. 

The  yoke  must  be  made  stiff  enough  to  prevent  sagging,  when 
built  up  with  its  poles  as  in  the  case  of  a  D.-C.  machine,  or  with 
its  stator  punchings  as  in  the  case  of  an  alternator  or  induction 
motor.  It  must  also  be  strong  enough  to  stand  handling  in  the 
shop  as,  for  example,  when  supported  as  shown  in  Fig.  311.  If 
the  yoke  will  stand  this  latter  treatment  it  will  generally  be  stiff 
enough  for  operating  conditions. 

499 


500 


ELECTRICAL  MACHINE  DESIGN 


The  following  rough  rule  may  be  used  for  checking  a  new  yoke 
design.     For  yokes  of  the  box  type  shown  in  Fig.  311, 


£  =  0.25  +QMDy  in.,  for  values  of  Dy  from  5  in.  to  100  in.  ; 
above  100-in.  bore  increase  the  thickness  by  0.375  in.  for  every  50 
in.  increase  in  diameter. 

The  distance  between  dovetails  should  be  about  12  in.,  for 
which  value  the  length  of  the  segment  used  to  build  up  the  core 
will  be  24  in.  It  is  at  present  standard  practice  to  dovetail  the 
laminations  into  the  yoke  as  shown  at  A,  but  the  method  shown 
at  B  has  been  found  satisfactory  and  has  the  advantage  over  A 
that  it  is  cheaper  and  does  hot  block  up  the  ventilation  so  much. 
The  distance  between  dovetails  is  determined  finally  by  the 
slot  pitch  and  the  number  of  slots  per  segment. 

344.  Rotors  and  Spiders.  —  These  must  be  designed  so  that 
they  will  stand  handling  in  the  shop. 


FIG.  312. — Stresses  in  pole  dovetails. 

The  rotor  of  a  revolving  field  alternator  is  usually  built  with 
the  poles  dovetailed  in,  as  shown  in  Fig.  312,  and  care  must  be 
taken  that  it  is  strong  enough  at  A  to  prevent  overstress  due  to 
its  own  centrifugal  force  and  to  the  bursting  action  of  the  pole 
dovetails,  and  also  strong  enough  at  B,  C,  D,  and  E.  The 
stresses  to  be  allowed  at  the  maximum  speed  are 

2500  Ib.  per  square  inch  for  cast  iron. 

12,000  Ib.  per  square  inch  for  cast  steel. 

14,000  Ib.  per  square  inch  for  sheet  steel. 

18,000  Ib.  per  square  inch  for  nickel  steel. 


MECHANICAL  DESIGN 


501 


The  arms  of  the  spiders  should  be  able  to  transmit  the  full-load 
torque  with  a  factor  of  safety  of  12,  then  they  will  be  strong 
enough  to  withstand  sudden  overloads  and  short-circuits. 

345.  Commutators. — Fig.  313  shows  a  typical  commutator. 
The  mica  between  segments  has  parallel  sides,  and  the  segments 
themselves  are  tapered  to  suit.  The  clamping  of  the  segments 
is  done  on  the  inner  surface  of  the  V  so  that  the  segments  will  be 
pulled  tightly  together,  and  the  design  should  be  strong  enough 


u 


V 


FIG.  313. — Construction  of  a  long  commutator. 


to  prevent  the  stresses  at  A,  B,  C,  D,  and  E  from  becoming  danger- 
ous. In  a  long  commutator  considerable  trouble  is  experienced 
due  to  the  expansion  and  contraction  of  the  bars  as  the  commu- 
tator is  heated  or  cooled,  and  the  type  of  construction  shown  is 
designed  to  take  care  of  such  expansion  by  the  extension  of  the 
bolts.  If  the  type  of  construction  shown  in  Fig.  27  were  used 
for  a  long  commutator  then,  when  the  commutator  is  heated  and 
expands,  the  shell  has  to  burst,  the  bolts  break,  or  the 
commutator  bars  bend. 

346.  Unbalanced  Magnetic  Pull.1 — If  two  surfaces  of  area  S 
sq.  cm.  have  a  magnetic  flux  crossing  the  gap  between  them, 
and  the  flux  density  in  this  gap  =  B  lines  per  square  centimeter, 
there  will  be  a  force  of  attraction  between  the  two  surfaces 

= — SB2  dynes. 

Fig.  314  shows  part  of  an  electrical  machine  of  which  the  revolv- 
ing part  is  out  of  center  by  a  distance  A  cm.  The  flux  density 
in  the  air-gap  at  C  is  greater  than  at  B}  so  that  the  magnetic 
force  acting  downward  is  greater  than  that  acting  upward. 

1  B.  A.  Behrend.    Transactions  of  A.  I.  E.  E.,  Vol.  17,  page  617. 


502 


ELECTRICAL  MACHINE  DESIGN 


The  resultant  downward  pull  is  called  the  unbalanced  magnetic 
pull  of  the  machine. 

In  the  following  discussion  it  is  assumed  that  the  flux  density 
in  the  air-gap  at  any  point  is  inversely  proportional  to  the  air-gap 
clearance  at  that  point,  and  also  that  the  eccentricity  is  not  more 
than  10  per  cent,  of  the  average  air-gap  clearance. 


and  B, 


FIG.  314. — Machine  with  an  eccentric  rotor. 

da  =the  air-gap  clearance  at  any  point  A 
—  ab  —  bc 
=  d-  A  cos  Q 
=  the  flux  density  at  point  A 


\  i 

df  *  =  the  force  at  A  over  a  small  arc  Rdd 


=  ~XBa*XRddXLc  dynes; 

07T 


and  the  vertical  component  of  this  force 


RLC  cos  Odd 


MECHANICAL  DESIGN  503 

=  —  RLCB2(  1+2-^  cos  #)cos  Odd]  higher  powers 
-r-  cos  6  than  the  first  being  neglected  since  -^  is  small,  being 


less  than  0.1. 

The  total  downward  force 


+  2y    COS0) 


cos  Odd 


similarly  the  total  upward  force 


The  total  unbalanced  magnetic  pull  is  the  difference  between  the 
total  downward  and  the  total  upward  force  and 

2 


c)£2      dynes 

O7T          0 

In  inch-pound  units  the  unbalanced  magnetic  pull  is  given  by 
the  following  formula  : 

Pull  in  pounds  ^(iSo)^  _  .  (69) 

where  B  is  the  effective  gap  density  in  lines  per  square  inch. 

A  is  the  displacement  in  inches 

d  is  the  average  air-gap  clearance  in  inches 

S  =  2nRLc,  is  the  total  rotor  surface  in  square  inches. 

Since  the  flux  density  in  the  air-gap  at  B  is  less  than  that  at  C, 

the  e.m.f.  generated  in  the  conductors  at  C  will  be  -greater  than 

that  generated  in  conductors  at  B.     If  a  multiple  winding  is  used 

for  the  rotor,  such  as  the  D.-C.  multiple  winding  or  the  squirrel- 

cage  winding  of  the  induction  motor,  then  the  current  in  each 

conductor  will  be  proportional  to  the  e.m.f.  generated  therein 

and  will  be  greater  in  conductors  at  C  than  in  those  at  B.     Now 

the  armature  current  in  a  D.-C.  machine  tends  to  demagnetize 

the  field  which  produces  it  and  so  also  does  the  current  in  the 

rotor  bars  of  an  induction  motor,  with  such  multiple  windings 

therefore  the  demagnetizing  effect  will  be  greatest  at  C  and  least 

at  B;  the  flux  in  the  air-gap  will  not  be  inversely  proportional  to 

the  air-gap;  and  the  magnetic  pull  will  be  less  than  that  given  by 

the  above  formula. 


504 


ELECTRICAL  MACHINE  DESIGN 


347.  Bearings,  Journals  and  Pulleys. — The  subject  of  bearing 
friction  has  already  been  discussed  in  Art.  79,  page  97. 

A  useful  rule  for  the  design  of  self-cooled  bearings  with  ring 
lubrication  is  that 

P  =  60  to  100;  PV  less  than  90,000  for  bearings  up  to  5  in, 
diameter 

P  =  40  to  60;  PV  less  than  60,000  for  bearings  above  5  in. 
diameter 

where  P  =  the  bearing  pressure  in  pounds  per  square  inch  pro- 
jected area 
V  =  the  rubbing  velocity  of  the  journal  in  feet  per  minute. 

Bearings  having  values  within  these  limits  will  carry  50  per 


FIG.  315.— Shaft  for  a  belted  machine. 

cent,  overload  without  injury;  if  the  values  at  normal  load  are 
greater  water-cooled  bearings  should  be  used. 

The  length  of  the  bearing  will  generally  be  from  3  to  4  times 
the  diameter,  but  the  stress  in  the  neck  of  the  journal  at  A}  Fig. 
315,  must  be  checked  to  see  that  it  is  not  too  high; 
if          Mb  =  the  bending  moment  at  A 
Mt  =  the  twisting  moment  at  A 
then      Me;  the  equivalent  bending  moment  at  A 


=  stress  X^d3 

this  stress  should  not  exceed  5000  Ib.  per  square  inch. 

The  shaft  at  the  center  is  designed  principally  for  stiffness. 
The  size  of  shaft  necessary  to  transmit  the  torque  is  compara- 
tively small;  the  actual  diameter  is  chosen  so  that  the  rotor  de- 
flection shall  not  exceed  10  per  cent,  of  the  air-gap  clearance; 
this  diameter  should,  however,  be  checked  for  strength  to  resist 
the  combined  effect  of  torsion  and  bending. 


MECHANICAL  DESIGN  505 

Fig.  315  shows  a  loaded  shaft.  W,  the  weight  between  the 
bearings,  includes  the  unbalanced  magnetic  pull,  and  Q  is  the 
total  pull  of  the  belt. 

If,  as  is  generally  the  case,  the  belt  is  in  contact  with  the 
pulley  over  half  the  circumference,  then 

T2  =  2  7\  approximately 
and  Q  =  T2  +  Z\ 

=  3T1  approximately 
„       _  h.  p.  X  33000 


belt  speed  in  ft.  per  min. 


The  total  force  on  the  bearing  next  the  pulley,  when  the  belt 
pull  is  vertically  downward  =1/2 


The  lower  the  speed  of  the  belt  the  greater  is  the  value  of 
T2—  Tl}  the  effective  force  on  the  belt,  and  the  greater  the  value 
of  Q,  so  that,  with  a  given  bearing,  there  is  a  minimum  diameter 
and  a  maximum  width  of  pulley  which  may  be  used  without 
overloading  the  bearing  or  overstressing  the  shaft. 

Consider  the  following  example.  Design  the  shaft  for  a  50-h.  p. 
900-r.p.m.  induction  motor. 

Air-gap  clearance  =0.03  in. 
Deflection  allowed  =  0  .  003  in. 
Rotor  weight          =  500  Ib. 
Rotor  diameter      =19  in. 
Frame  length          =  6  .  5  in. 
Carter  coefficients  =  1  .52 

S,  in  formula  69     =  ?rX  19X6.  5X™  =255  sq.  in. 

Max.  flux  per  pole  =  1  .  04  X  106 

,..        «       j       ..         flux  per  pole  X  poles     TT 
Max.  flux  density  =  -          —  ^  —  —  Xs 

n 
X 


255  2 

=  51,000  lines  per  square  inch. 

(T?     \    2        f^  1  2 
1000)  =^ 

Unbalanced  pull  =  ==  X255  X1300  xO.l 

=  460  Ib. 

=  460  +  500  =  960  Ib. 

The  deflection  is  limited  to  0.1X0.03  =  0.003  in. 
W  X(2L)3 


and  deflection  = 


48XEXI 


506  ELECTRICAL  MACHINE  DESIGN 

where  2L   =the  distance  between  bearings  in  inches,  see  Fig.  315 
E  =  Young's  modulus  =  30,000,000  in  inch-pound  units 
I  =  the  moment  of  inertia  to  bending 

4 § 

therefore  da,  the  necessary  shaft  diameter  =  \ /      X^- — L 

\7xW6Xd 

960  X193 


'7X106X0.03 
=  2.4  in.  approximately 

Assume  now  that  the  belt  speed  =  4000  ft.  per  minute,  then 
the  pulley  diameter  =  17  in. 
50  X  33000 


4000 
414  Ib. 


, 


the  maximum  pull  in  the  belt  =  T2 

=  2Tl 
=  828  Ib. 

the  belt  width  =  10  in.  and  the  belt  stress  =  83  Ib.  per  inch  width. 

For  a  single  belt  the  stress  should  be  less  than  45  Ib.  per  inch  width  and 
for  a  double  belt  should  be  less  than  90  Ib.  per  inch;  a  double  belt  should 
not  be  used  on  a  pulley  smaller  than  12  in.  in  diameter.  With  a  10-in.  belt 
and  the  pulley  overhung,  the  smallest  possible  value  for  C,  Fig.  315  =  10-in. 
The  value  of  Q  =  3x414  =  1240  Ib. 


The  belt  pull  on  the  bearing  = 

=  19001b. 

1/2TF  =  480    Ib. 

Total  bearing  pressure  =23801b. 

Size  of  bearing  =3x9  and  the  value  of  P  =  88  Ib.  per  square  inch 

and  PV  =  62,000 

The  stress  in  the  shaft  must  now  be  determined. 

The  bending  moment  at  M  =Q  X  10 

=  1240X10 

=  stress  X  ^d3 

therefore  the  stress  at  the  neck  of  the  journal  =4700  Ib.  per  square  inch. 

The  shaft  will  be  cut  out  of  3  1/2  in.  stock  and  the  journals  turned  down 

to  3  in.;  the  deflection  will  be  less  than  10  per  cent,  of  the  air-gap  clearance. 

348.  Brush  Holders.  —  The  more  important  of  the  conditions 
to  be  fulfilled  by  the  brush  holder  are  that  it  should  be  rigid 
enough  not  to  be  set  in  vibration;  that  it  must  bear  on  the  brush 
with  a  tension  which  may  be  adjusted;  that  it  must  be  adjustable 
for  wear  of  the  brushes;  that  the  brush  and  that  part  of  the  holder 
which  is  attached  to  it  must  not  have  too  great  an  inertia,  because 


MECHANICAL  DESIGN 


507 


the  brush  has  to  move  with  the  commutator  if  the  latter  does  not 
run  perfectly  true. 

Two  holders  much  used  in  practice  are  shown  in  Figs.  316  and 
317.     In  the  former  the  brush  is  clamped  to  the  holder,  while  in 


FIG.  316. 


FIG.  317. — Brush  holders. 


the  latter  it  is  free  to  slide  in  a  box  and  therefore  requires  a  pig- 
tail A  of  stranded  copper  to  carry  the  current  to  the  holder, 
otherwise  this  current  would  pass  along  the  spring  B  and  draw 
its  temper. 


508 


ELECTRICAL  MACHINE  DESIGN 


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LIST  OF  SYMBOLS 

Used  along  with  these  symbols  the  suffix  ^stands  for  stator  or  primary 
and  the  suffix  2  for  rotor  or  secondary. 

Unless  otherwise  stated  the  dimensions  are  in  inch  units. 

PAGE 

A            =  brush  contact  area 98 

Aag        =  actual  gap  area  per  pole      43 

Ab           =  projected  area  of  bearing 97 

AC           =  core  area 43 

A  g          =  apparent  gap  area  per  pole 43 

Ap          =  pole  area 43 

Ar           =  section  of  end  connector 372 

At           =  tooth  area  per  pole 43 

Ay          =  yoke  area 43 

AT         =  ampere  turns. 

ATt        =  ampere  turns  per  pole  for  the  core 49 

AT g       =  ampere  turns  per  pole  for  the  gap 48 

AT g+t    =  ampere  turns  per  pole  for  gap  and  tooth 51 

A  Tmax  =  ampere  turns  per  pole,  maximum  excitation 238 

ATp       =  ampere  turns  per  pole  for  the  pole  core 48 

ATt        =  ampere  turns  per  pole  for  the  teeth 48 

ATy       =  ampere  turns  per  pole  for  the  yoke 46 

B            =  flux  density 6 

Bag        =  actual  gap  density \ 45 

Bat         =  actual  tooth  density 45 

Bc           =  core  density 45 

Bff          =  apparent  gap  density 45 

Bi           =  interpole  gap  density 94 

Bm          =  maximum  flux  density  in  transformer  cores 441 

Bp          =  pole  density 45 

BI           =  apparent  tooth  density 45 

By          =  yoke  density      45 

B.  &  S.=  Brown  and  Sharp  gauge. 

C            =  Carter  fringing  constant 43 

Da          =  armature  external  and  stator  internal  diameter 42 

Dc          =  commutator  diameter Ill 

Dr           =  mean  diameter  of  rotor  end  connector 372 

E  =  volts  per  phase. 

EU         =  component  of  applied  e.m.f.  equal  and  opposite  to  the  back 

generated  e.m.f .  331 

Erf         =  back  generated  e.m.f.  in  primary 329 

Ef          =  volts  per  field  coil 65 

E8           =  generated  voltage  in  the  short  circuited  coil 85 

Et           =  terminal  voltage 169 

33  513 


514  ELECTRICAL   MACHINE  DESIGN 

PAGE 

F  =  commutator  face Ill 

F  =  finish  of  winding 161 

7  =  amperes  per  phase. 

7n  =  component  of  primary  current  with  a  .m.m.f.  equal  and  oppo- 
site to  that  of  the  secondary  current 331 

Ia  =  armature  current 103 

7C  =  current  per  conductor 55 

Id  =  maximum  current  in  induction  motors 337 

Ie  =  exciting  current 343,  427 

If  =  field  current       42 

Ii  =  line  current 169 

Im  =  magnetizing  current .    .    .  • 428 

I0  =  magnetizing  current     . 329 

78C  =  short  circuit  current 344 

K  =  hysteresis  constant 100 

Kl  =  reactance  constant 369 

K2  =  reactance  constant 369 

Ke  =  eddy  current  constant 100 

K.V.A.  =  kilo  volt  amperes. 

K.W.  =  kilowatts. 

L  =  length  of  transformer  coils 445,  448 

L  =  coef.  of  self  induction 75 

L/b  =  length  of  conductor      102 

Lc  =  axial  length  of  core 43 

Le  =  length  of  end  connections 108 

Lf  =  radial  length  of  field  coil 65 

Lg  =  gross  iron  in  frame  length 43 

Lip  =  axial  length  of  interpole 94 

Ln  =  net  iron  in  frame  length 43 

Lp  =  axial  length  of  pole 43 

L8  =  axial  length  of  pole  shoe 51 

M  =  section  in  circular  mils 65 

M  =  coef.  of  mutual  induction 75 

MT  —  mean  turn  of  coil      65 

MT  =  mean  turn  of  transformer  coils 448 

N  =  number  of  slots 43 

P.P.  =  power  factor. 

R  =  reluctance. 

R  =  resistance  per  phase. 

R  =  brush  contact  resistance      .    . 75 

fte  =  equivalent  secondary  resistance 431 

Reg  =  equivalent  primary  resistance 431 

R.  V.  =  reactance  voltage      . 121 

S  =  number  of  commutator  segments 18 

S  '=  space  between  high  and  low  voltage  coils 445,  448 

S  =  start  of  winding 161 

•S  =  total  rotor  surface     .                                                                     .  503 


LIST  OF  SYMBOLS  515 

PAGE 

T  =  time  constant 376 

T  =  turns  per  coil. 

Tc  =  time  of  commutation 75 

Tf  =  field  turns  per  pole .  42 

V  =  air  velocity  in  ft.  per  min 106 

V  =  peripheral  velocity  of  rotor  in  1000s  of  ft.  per  min 396 

Vb  =  rubbing  velocity  of  bearing 97 

V ' r  =  rubbing  velocity  of  brush 98 

W  =  weight  of  iron  in  Ib 100 

Wip  =  irxterpole  waist 93 

Wp  =  pole  waist 43 

W8  =  width  of  pole  shoe 52 

X  —  leakage  reactance  per  phase 211 

X  =  synchronous  reactance 214 

X2  =  rotor  reactance  at  standstill 330 

Xe  =  equivalent  secondary  reactance 431 

Xeq  =  equivalent  primary  reactance 431 

Z  =  total  face  conductors  in  D-C.  armatures 11 

Z  =  conductors  in  series  per  phase 189 

Zc  =  total  number  of  conductors  in  alternators 248 

a  =  slots  per  pole 184 

b  =  conductors  per  slot 216 

c  =  slots  per  phase  per  pole 216 

cos  0  =  power  factor 169 

d  =  slot  depth 43 

dvd2,d3,di  =  slot  dimensions 218 

dl}  d2  =  dimensions  of  transformer  coils 445,  448 

da  =  depth  of  armature  core 43 

db  =  bearing  diameter 97 

df  =  depth  of  field  winding 65 

d8  —  shaft  diameter 278 

d.c.c  =  double  cotton  covering  on  wires. 

e  =  volts  per  conductor 188 

/  =  frequency 162 

/  =  constant  in  Carter  formula 43 

hp  =  height  of  pole 52 

h8  =  height  of  pole  shoe 51 

h.p.  =  horse-power. 

i  =  current  in  amperes. 

k  =  constant  in  reactance  voltage  formula      84 

k  =  distribution  factor 189 

k  =  a  whole  number,  in  winding  formula 18 

kr  =  end  ring  resistance  factor 372 

magnetic  loading  in  transformers 

™l                                            \      ~;      ; T~.                              47o 

electnc  loading 

(—!&)  =  per  cent,  of  copper  in  a  given  thickness  of  winding.    ....  473 

k.v.a.  =  kilo  volt  amperes      188 


516  ELECTRICAL  MACHINE  DESIGN 

PAGE 

k.w.  =  kilowatts. 

lv  —  length  of  leakage  path 51 

Z3  =  length  of  leakage  path 52 

lh  =  length  of  bearing 97 

lc  =  magnetic  length  of  core 49 

lp  =  magnetic  length  of  pole  core 48 

ly  =  magnetic  length  of  yoke      46 

If.  =  leakage  factor 49 

m.m.f.  =  magneto-motive  force. 

n  =  number  of  phases. 

p  =  number  of  poles. 

pl  =  number  of  paths  through  the  armature 11 

q  =  ampere  conductors  per  inch 114,255 

r.p.m.j   =  synchronous  speed  of  induction  motors 333 

r.p.m.2   =  rotor  speed 330 

s  =  per  cent,  slip 328 

s  =  slot  width 43,  219 

sf.  =  space  factor 65 

t  =  thickness. 

t  =  time  in  sees. 

t  =  tooth  width 43,  221 

v2  =  leakage  constant  in  induction  motors 334 

w  =  slot  width 218 

d  =  air-gap  clearance 43 

y  =  efficiency. 

A  =  slot  pitch .    .      43 

Xe  =  distance  the  end  connections  project 108 

T  =  pole-pitch 42 

$  =  magnetic  flux. 

(j)a  =  useful  flux  per  pole 11,  178 

(f)a  =  flux  in  transformer  core  at  no-load 439 

<jte  =  leakage  flux  between  poles      42 

(f>e  =  end  connection  leakage  constant 79,  215,  360 

(f>m  —  total  flux  per  pole 42 

<£8  =  slot  leakage  constant 79,  216,  360 

(f)t  =  tooth  tip  leakage  constant 216 

<f>ta  =  tooth  tip  leakage  constant 221 

<f>tp  =  tooth  tip  leakage  constant 221 

(j)z  =  zig  zag  leakage  constant      360 

(f>  =  per  cent,  pole  enclosure 42 


INDEX 


Ageing  of  iron,  440 

Air  blast  for  cooling,  281,  469 

ducts,  armature,  24,  28,   192, 

349 

field  coils,  40 

films  in  insulation,  198,  201 
gap,  area,  43 

clearance,   67,   69,   229,   240, 

243,  260,  394,  403 
flux  density  in,  45,  94,   114, 

256,  288,  393 
distribution  in,  44,   54-58, 

209,  288,  358 
fringing  constant,  43 
Alloyed  iron,  100,  440 
Alternating  and  rotating  fields,  186 
Alternator,  construction,  191 

current  density,  252,  253,  262, 

•     293 

field  system  design,  237 
flux    densities,    229,    245,    252, 

257,  282,  289 
generated  e.m.f.,  178 
heating,  239,  252-254,  279-282 
insulation,  193,  203-207 
losses,  247-251 

procedure  in  design,  255 

ratings,  188,  236 

reactance  of  armature,  215-226, 
233-236,  285 

reactions  of  armature,  208-236, 
289 

slots,  180,  256,  260,  262 

specifications,  312 

turbo,  273 

vector  diagrams,  210-212 

windings,  160 
Amortisseurs,  295,  303 
Ampere  conductors,  115 

conductors  per  inch,   109,  115, 
146,  241,  256,  258,  381,  394 

turns,  4 


Ampere  turns  per  pole,  armature,  61, 

91,  147,  230,  290 
cross  magnetizing,  55-61,  146, 

209 
demagnetizing,    59,    149,    209,. 

214,  232,  289 
field  excitation,  46-51,  67,  237, 

238,  290,  308 
interpole  field,  92,  94,  151 
series  field,  68 
Areas,  magnetic,  42,  359 
Armature,    D.-C.,    construction,   24, 

153 
current  density,   109-111,   123, 

131 

flux  densities,  45,  107,  1.14 
generated  e.m.f.,  11 
heating,  104 
insulation,  36 
losses,  97 

peripheral  velocity,  142,  144 
procedure  in  design,  114,  147 
reaction,  54 
resistance,  102 
slots,  24,  87,  123 
strength  relative  to  field,  61,  87 

91,  146 
winding,  7 
Asbestos,  274 
Average  volts  per  bar,  95,  138,  143 

Back  e.m.f.,  323 

Bearing,  construction,  27,  29 

design:  97,  504 

friction,  97,  344,  357 

housings,  25,  350 

oil  temperature,  98,  314 
Belt  leakage,  332,  365 
Blackening     of     commutator     seg- 
ments, 87 

Break  down  point,  328 
Breathing  of  coils,  201 


517 


518 


INDEX 


Brush,  arc,  9,  80,  88,  91,  94,  148 

contact  resistance,  76 

current  density,  75,  78,  194 

friction,  98 

holders,  506 

number  of  sets,  12,  18 

pressure,  78 
Bushings,  transformer,  435,  451 

Carter  fringing  constant,  43 
Cast  iron,  magnetic  properties,  47 

stresses  in,  500 
steel,  magnetic  properties,  47 

stresses  in,  500 

Centrifugal  force  of  turbo  rotors,  275 
Chain  windings,  169 
Characteristics,  424 

and  frequency,  392,  410,  420, 

493 
and  speed,   157,  316,  392,  409, 

426 
and  voltage,  156,  315,  420,  424, 

425,  496 

Circle  diagrams,  333-347 
Cir.  mils  per  ampere,  109-111,  123, 

252,  293,  380,  381,  475 
Circulating  current  in  brushes,    13, 

90 
in  windings,   13,    19,    164,    173, 

184,  297 

Closed  slots,  24,  348,  411 
Coils,  armature,  22,  36-39,  108, 153, 

203-207,  250 
field,  40,  62,  68,  193 
groups,  36 

transformer,  434,  438,  455,  461 
Commutation,     best     winding     for 

sparkless,  140 
guarantee,  155 
perfect,  76 
selective,  19 
theory,  72 

with  duplex  windings,  9 
interpoles,  92 
series  windings,  19,  83 
short  pitch  windings,  15,  82 
Commutator,  construction,  27,   153 
sign,  121,  124,  148 


Commutator,  diameter,  120 
heating,  111 
insulation,  27 
length,  139,  148 
losses,  98,  103 
mechanical  design,  501 
number  of  segments,  18,  138 
peripheral  velocity,  120 
ventilation,  27,  111 
voltage  between  segments,  138, 

143 

wearing  depth,  120 
Compensating  fields  coils,  96,  144 
Condenser  bushings,  453 
Conductors,  current  density  in,  109- 
111,123,252,293,380,381, 
475 

eddy  currents  in,  248,  372,  461 
lamination  of,  248,  249,  461 
number  of,  121,  127,  130,  260, 

267,  397,  407 
Construction  of  alternators,  191,  272, 

312 

D.-C.  machines,  24,  153 
induction  motors,  323,  348,  422 
transformers,  433,  494 
Contact  resistance,  76 
Cooling.     See  Heating, 
by  convection,  106 
Copper  loss,  armatures,  102,  248 
field  coils,  103,  247 
induction  motors,  371 
transformers,  461,  481 
resistance  of,  102 
Core,  flux  density  in  alternator,  252, 

282 

in  D.-C.  armature,  45,  107 
in  induction  motor,  358,  381 
in  transformer,  479 
or  iron  loss,  99,  355,  439,  442, 

443 
type  transformers,  construction, 

433 

heating,  464 
insulation,  458 
procedure  in  design,  478 
reactance,  445,  482 
three-phase,  490 


INDEX 


519 


Corrugated  tanks,  467 
Cotton,  30 

covering  for  wire,  31,  508 
Creepage,  surface,  34,  450,  454,  455, 

456 

Critical  speed  of  turbo  rotors,  278 
Cross    magnetizing    ampere    turns, 

55-61,  146,  209 

Current  density  in  alternator  wind- 
ings, 252,  253,  262,  293 
in  brush  contacts,  75,  78,  194 
in  D.-C.  armatures,  109-111, 

123,  131 

in  field  coils,  69,  70,  151,  379 
in  induction  motors,  380,  381, 

397,  407 

in  transformers,  475 
direction,  1 
maximum  in  induction  motors, 

337,  363,  394,  395, 
relations  in  induction   motors, 

323,  331,  335 
in  transformers,  429 
Curves  of  amp.  cond.  per  inch,  115, 

257,  393 
of  armature  and  stator  heating, 

115,  253,  382 
of    efficiency,    158,    159,    318, 

392 

of  field  coil  heating,  64,  239 
of  gap  density,  115,  257 
of  iron  loss,  102,  442 
of  magnetization,  47,  48,  442 
of  power  factor,  392 
of  saturation,  50,  60,   237,   309, 

343 

of  short  circuit,  225,  343 
of  space  factor,  65 
of  transformer  heating,  466.  468 

D2L,  114,  255,  391 
Dampers,  295,  303 
Dead  coils,  22,  130 

points  at  starting,  310,  388 
Delta  connection,  163,  407 

and  harmonics,  183 
Demagnetizing    ampere    turns,    59, 
149,  209,  214,  232,  289 


Density  of  current  in  alternator 
windings,  252,  253,  262, 
293 

in  brush  contacts,  75,  78,  194 
in  D.-C.  armatures,  109-111, 

123,  131 

in  field  coils,  69,  70,  151,  379 
in  induction  motors,  380,  381, 

397,-  407 

in  transformers.  475 
of  flux,  and  m.m.f.,  5 

in  air  gap,  45,  94.   114,  256, 

288,  393 

in  armature  and  stator  cores, 
45,  107,  252,  282,  358,  381 
in  pole  cores,  45,  67,  229 
in  rotor  cores,  381 
in  teeth,  45,  46,  107,  252,  282, 

358,  381 

in  transformer  cores,  479 
in  yoke,  45,  67 

Design  procedure  for  alternators,  255 
for  d.-c.  generators,  114 
for  d.-c.  motors,  127 
for  field  system,  62,  237 
for  induction  motors,  391 
for  interpole  machines,  146 
for  synchronous  motors,  308 
for  transformers,  476 
for  turbo  alternators,  290 
Diameter  of  armature  or  stator,  116, 
120,  141,  143,  257,  259,  393 
Dielectric  flux,  195 
strength,  30,  196 
of  cotton,  30 
of  empire  cloth,  32 
of  micanite,  31 
of  oil,  449 
of  paper,  32 
Dimensions     and    frequency,     415, 

493 

and  output,  114,  255,  391 
Direction  of  current,  1 
of  e.m.f.,  3 

of  magnetic  lines,  1,  2 
Distributed  windings,  171,  180,  187 
Distributing  transformer,  433,  463, 
476,  487 


520 


INDEX 


Distribution  factor,  189 

of  magnetic  field,  gap,  44,  54- 

58,  209,  288,  358 
core,  101,  358 
Double  frequency  harmonics,  231 

layer  windings,  13,  170 
Doubly  re-entrant  windings,  8 
Dovetails,  28,  192,  193,  351,  500 
Drum  windings,  9 
Ducts  in  armature  and  stator  cores, 

24,  28,  192,  349 
in  field  coils,  40 
in  transformer,  435,  472 
Duplex  windings,  8,  20 

Eddy    currents    in    armature    and 

stator  cores,  100, 
in  conductors,  248,  372,  461 
in  pole  shoes,  101,  295 
in  transformer  cores,  439,  444 
Efficiency,  effect  of  speed,  157,  316, 

392,  426 
of  voltage,  156,  315,  420,  425, 

496 

of  alternators,  251,  313,  318 
of  d.-c.  machines,  97,  132,  158, 

159 

of  induction  motors,  392,  423 
of  transformers,  463,  497 
Electric  loading,  116,  147,  476 
Electrical  degrees,  162 
Electromotive  force,  2 
direction  of,  3 
in  alternators,  178,  189 
in  d.-c.  machines,  11 
in  induction  motors,  352 
in  transformers,  439 
Empire  cloth,  32 
Enclosed  machines,  350 
heating  of,  134,  383 
rating  of,  133 
End  connection  heating,   108,  252, 

254,  381 

Insulation,  34,  207 
leakage,  217 
length,  108 
supports,  287,  350 
play  for  shafts,  25 


End  rings,  loss  in  induction  motor, 

371 

section,  399 
turns,  insulation  of  transformer, 

456 

Equalizer  connections,  13,  22 
Equivalent  reactance,  induction  mo- 
tor, 337,  363 
transformer,  431,  447 
resistance,  431 
Even  harmonics,  183 
Excitation,    calculation   of  no-load, 

46,  242 

of  full  load,  59,  246 
of  induction  motor,  357 
of  transformer,  440,  481,  485 
effect  of  power  factor,  237 
for  joints,  444 
synchronous  motor,  306 
Exciter,  193,  311,  312 
Exciting  coils,  25,  193 

current,  352,  357,  394,  440,  481, 
485 

Fans,  25,  252,  273,  351 
Field  coils,  compensating,  96,  144 
construction,  40,  68,  193 
design  procedure,  62,  237 
heating,  62,  239 
insulation,  40.  193 
interpole,  150 
losses,  103,  133,  237,  247 
ventilation,  40,  64,  193 
magnetic,    distribution  in  gap, 

44,  54-58,  209,  288,  358 
in  core,  101,  358 
leakage  between  poles,  42,  51, 

213 

in  alternators,  215,  233 
in  induction  motors,  360 
in  transformers,  445 
relation    between    main   and 

armature,  61,  229,  290 
magnets,  construction,  25,    192 
dimensions,  25,  65,  67,  238 
flux  density,  45,  67,  229 
turbo,  275 
Flashing  over,  95 


INDEX 


521 


Fleming's  rule,  3 

Flux  distribution  in  air  gap,  44,  54- 

58,  209,  288,  358 
in  armature  core,  101,  358 
density,  and  m.m.f.,  5 

in  air  gap,  45,  94,  114,  256, 

288,  393 

in  armature  and  stator  cores, 
45,  107,  252,  282,  358,  381 
in  pole  cores,  45,  67,  229 
in  rotor  cores,  381 
in  teeth,  45,  46,  107,  252,  282, 

358,  381 

in  transformer  cores,  479 
in  yoke,  45,  67 
pulsations,  184,  386 
Flywheels,  297-303,  315 
Forced  draft,  281,  469 

oscillations,  298,  302 
Form  factor,  178,  439,  440 
Fractional  pitch  winding,  15,  82,  181, 

189,  419 
Frequency  and  characteristics,  392, 

410,  420,  493 
and  dimensions, '41 5,  493 
speed  and  poles,  162,  322 
Friction  in  bearings,  97,  344,  357 

in  brushes,  98 
Fringing  of  flux,  43 
Full-load  saturation,   59,   212,   227, 

237,  309 
Fullerboard,  450,  457,  458 

Gap.     See  Air  gap. 

Grading  of  insulation,  199 

Gramme  ring  winding,  7,  9 

Grounds,  33 

Guarantees,  commutation,  135,  155 

efficiency,  154,  313,  423,  495 

overload    capacity,    135,    155, 
314,  424 

power  factor,  392,  423 

temperature,  133,  155,  314,  424, 
496 

regulation,  313,  495 

Harmonics  in  the  e.m.f.  wave,  178 


Harmonics,    in    the    magnetic  field, 

184,  231,  295,  418 
Heat,  effect  on  insulation,  31,  33,  104 
Heating  and  cooling  curves,  375 
and  construction,  252,  382 
of  alternator  rotors,  239 

stators,  252 
of  commutators,  111 
of  dampers,  305 
of  d.-c.  armatures,  104 
of  enclosed  machines,  134,  382 
of  field  coils,  62,  239 
of  high  voltage  coils,  109,  250, 

253 

of  induction  motors,  375 
of  oil  in  bearings,  98,  314 
of  semi-enclosed  machines,  383 
of  transformers,  463 
of  turbos,  274,  279,  295 
High  speed  alternators,  272 
induction  motors,  414 
limitations  in  design,  141,  417 
torque  ratings,  382 
voltage  insulation  for  alterna- 
tors, 201,  205 

for  transformers,   459,   488 
limitations  in  design,  138,  488 
due  to  harmonics,  179 
Horn  fibre,  32 
Housings,  25,  350 
Humming,  385,  416,  434 
Hunting  of  alternators,  298,  314 
of  synchronous  motors,  308 
Hysteresis  loss,  100,  439,  440 

Impedence  of  windings.     See  React- 
ance. 
Impregnating    compound,    31,    32, 

201,  450 
Induction  motor,  construction,  348 

current  density,  380,  381 

excitation,  352,  357 

flux  densities,  358,  381,  393 

generated  e.m.f.,  352 

heating,  375 

insulation,  203 

losses,  355,  371 

noise,  385 


522 


INDEX 


Induction  motor,  peripheral  velocity, 

416 

procedure  in  design,  391 
reactance,  360 
slots,  356,  386,  387,  389,  391, 

397,  398,  416 
specifications,  422 
starting  torque,  388 
theory  of  operation,  319 
vector  diagrams,  329,  333 
windings,  322 

Insulating  materials,  canvas,  40 
cotton,  30,  31 
empire  cloth,  32 
fibre,  32 

fullerboard,  450,  457,  458 
impregnating  compound,  31,  32, 

201,  450 
micanite,  31 
mica  paper.  201 
oil,  449 
paper,  32 
pressboard,  450 
silk,  31 
tape,  30 
varnish,  32,  450 
wood,  450 
Insulation,  air  films  in,  198,  201 

chemical   effects  in  high   volt- 
age, 201 

condenser  type,  453 
creepage  across,  34,  450,  454, 

455,  456 

dielectric  strength,  30,  196 
effect  of  heat,  31,  33,  104 

of  moisture,  30,  32,  449 

of  time,  200 

of  vibration,  33 
grading  of,  199 
potential  gradient,  196,  198, 

200,  452 

puncture  test,  30,  34,  424,  496 
specific    inductive    capacity, 

197,  198,  201 
thickness  of,  32,  39,  101,  203, 

205,  206,  459 
Insulation  of  armature  and  stator 

coils,  36,  203 


Insulation  of  commutators,  27 
of  end  connections,  34,  207 
of  field  coils,  40,  193 
of  rotor  bars,  411,  424 
of  transformers,  438,  449 
of  turbo  rotors,  274 

Intermittent  ratings,  379 

Interpole  ampere  turns  per  pole,  92, 

94,  151 

dimensions,  93,  150 
field  system  design,  149 
machines,  92,  137,  140 
limit  of  output,  142 
procedure  in  design,  146 

Iron,  ageing  of,  440 
alloyed,  100,  440 
losses.  99,  355,  439,  442,  443 
magnetization    curves,    47,    48, 

442 

thickness   of  laminations,    100, 
191,  348,  350,  440 

Joints  in  magnetic  circuit,  433,  436, 

444 
Jumpers,  170 

Kilo  volt  amperes,  188 

Lag  of  current  in  induction  motors, 

325,  327 

synchronous  motors,  306,  307 
Lamination  of  conductors,  248,  249, 

461 
of  core  bodies,  24,  28,  100,  191, 

348,  350,  440 
of  pole  faces,  25,  101 
Laminations,  thickness  of,  100,  191, 

348,  350,  440 
Lap  windings,  20 
Lead    of    current    in    synchronous 

motors,  306,  307 
Leakage  factor,  no-load,  42,  51,  53, 

244 

full-load,  213,  244 
field,  belt,  332,  365 

end  connection,  215,  217 
pole,  42,  51,  213 
slot,  215,  218 


INDEX 


523 


Leakage  field,  tooth  tip,  216,  220 
transformer  coils,  428,  445 
zig  zag,  361,  387 
reactance  in    alternators,    215, 

233,  285 

in  induction  motors,  360 
in  transformers,  445,  482 
Length  and  diameter  of  armatures, 

11.6,  257,  264,  393,  404 
of  air  gap,  67,  69,  229,  240,  243, 

260,  394,  403 
of  armature  coils,  108 
Limitations  in  design,  high  voltage, 

138,  488 

large  current,  139 
low  voltage,  294 
speed,  141,  272,  417 

Lines  of  force,  1 

Loading,  electric  and  magnetic,  116, 

147,  476 

Locking  points  at  starting,  310,  388 
Losses,  constant,  337 

copper,    102,   248,   338,   371, 
461 

contact  resistance,  103 

eddy    currents    in    conductors, 
248,  372 

field  coils,  103,  247 

friction,  97,  98 

in  alternators,  247 

in  d.-c.  machines,  97 

in  induction  motors,  355,  371 

in  transformers,  439,  461 

iron,  99,  355,  439 

load,  251 

pulsation,  355 

rotor  end  ring,  371 

windage,  98 
Low  voltage  limitations  in  design, 

139,  294 

Magnet  coils.     See  Field  Coils. 
Magnetic  areas,  42,  359 

circuit,  example  of  calculation, 

42 
field,  distribution  in  gap,  44,  54- 

58,  209,  288,  358 
in  core,  101,  358 


Magnetic  field,    leakage   between 
poles,  42,  51,  213 

in  alternators,  215,  233 
in  induction  motors,  360 
in  transformers,  445 
relation  between  main  and 
armature,  61,  229,  290 
Magnetic  loading,  116,  147,  476 
potential,  4 
pull,  unbalanced,  501 
Magnetization  curves,  47,  48,  442 
Magnetizing    current    in    induction 

motors,  352,  357,  394 
in  transformers,  440,  481,  485 
Magnetomotive  force,  4 
Maximum     current     in     induction 
motors,  337,  363,  394,  395 
output,  341,  347,  409,  424 
temperature  rise,  62,  104,  464, 

473 

torque,  328,  341,  347 
Mechanical  design,  499 
Mica  for  commutators,  27 
Micanite,  31 
Mica  paper,  201 

Moisture  and  insulation,  30,  32,  449 
Motors,   d.-c.,   procedure  in  design, 

127 

ratings,  129,  133,  135 
Motors.     See    Induction   and   Syn- 
chronous. 

Multiple  windings,  16,  21,  79,  140 
Multiplex  windings,  8 

Natural    frequency    of    alternators, 

298,  303 
Nickel  steel,  500 
Noise  in  induction  motors,  385,  416 

in  transformers,  434 
No-load   current.     See  Magnetizing 

Current, 
saturation  curve,  46,  240,  342 

Oil  for  transformers,  449 

Output  and  dimensions,    114,   255, 

391 

limits,  high  voltage,  138,  488 
large  current,  139 


524 


INDEX 


Output  limits,  low  voltage,  294 

,     speed,  141,  272,  417 
"    maximum,  341,  347,  409,  424 

of  three-phase  alternators,  169 
Over     excitation     of     synchronous 

motors,  306 
Overload  capacity,  78,  135,  155,  314, 

424 
Overspeed  requirements.  272 

Pancake  coils,  466 

Paper,  32 

Parallel  operation  of  alternators,  297 

Peripheral    velocity    of    armatures, 

142,  144 

of  commutators,  120 
of  rotors,  272,  275,  290,  416 
Pitch  of  poles,  42,  117,  258 

of  slots,  43,  87,  123,  256,  357, 

386,  389,  391 
of  windings,  15,  20 
Pole  arc  and  harmonics,  178 

construction,  25,  28,   101,   192, 

275 

dimensions,  25,  65,  67,  238 
enclosure,  42,  49,  91.  259 
face  and  wave  form,  180 
flux  density,  45,  67,  229 
number  of,  117,  162,  322 
pitch,  42 
pitch  and  characteristics,   409, 

410 
Potential  gradient,  196,  198,  200,  452 

starter,  423 
Power  factor  and  armature  reaction, 

208,  226 

and  excitation,  237 
and  frequency,  392,  410.  420 
and  speed,  392,  409,  426 
and  voltage,  420,  425 
correction     by     synchronous 

motors,  306 

in  three-phase  machines,  169 
Pressboard,  450 
Pressure  on  bearings,  504 

on  brushes,  78 

Procedure  in  design  of  alternators, 
255 


Procedure  in  design  of  d.-c.  genera- 
tors, 114 
motors,  127 
field  system,  62,  237 
induction  motors,  391 
interpole  machines,  146 
synchronous  motors,  308 
transformers,  476 
turbo  alternators,  290 

Progressive  windings,  18 

Pulley  design,  504 

Pulsations  of  magnetic  field,  184,  386 

Puncture  tests,  30,  34,  424,  496 

Ratings,  d.-c.  motors,  129,  133,  135 
high  torque  induction  motors, 

382 

intermittent,  379 
single   and   polyphase    alterna- 
tors, 188,  236 

Ratio  of  transformation,  428 
Reactance  of  alternators,    215,   233, 

285 

of  induction  motors,  360 
of  transformers,  445,  482 
synchronous,  213 
voltage,  limits,  90,  138,  143,  146 
of  interpole  machines,  149 
of  non-interpole  machines,  79 
Reaction,    armature,    in    d.-c.    ma- 
chines, 54 
in   polyphase  alternators,   208, 

289 

in  single  phase  alternators,  231 
Re-entrant  windings,  8 
Regulation,  and  size  of  machine,  241 
effect  of  air  gap  on,  229 
of  pole  saturation  on,  228 
of  power  factor  on,  246 
in  synchronous  motors,  308 
of  alternators,  228,  236,  313 
of  transformers,  431,  489,  495 
Resistance  of  alternator  and  stator' 

windings,  102,  248 
of  brush  contacts,  76 
of  copper,  102 
of  field  coils,  65 
of  induction  motor  rotor,  371 


INDEX 


525 


Resistance  of  transformer,  461 

starting    in    induction    motors, 

327,  382 

Resonance  between  machines  hunt- 
ing, 315 

in  electric  circuits,  179 
Retrogressive  windings,  19 
Reversing  of  induction  motors,  319 
Revolving  field  in  induction  motors, 

319,  333 

type  of  alternator,  191 
Ring  winding,  7,  9 
Rocker  arm,  27 

Rotating  and  alternating  fields,   186 
Rotor    of    alternator,    construction, 

192,  275 

current  density,  238,  243 
flux  density,  229,  245 
heating,  239,  274,  279 
insulation,  193,  274 
losses,  247 
peripheral  velocity,  272,  275, 

290 

procedure  in  design,  237,  291 
strength  relative  to  armature, 

230,  290 
turbo,  275 

of   induction   motor,    construc- 
tion, 323,  350,  422 
current  density,  380,  381 
effect  of  resistance,  327,  382 
flux  density,  358,  381 
heating,  381 
insulation,  411,.  424 
losses,  355,  371 
peripheral  velocity,  416 
procedure  in  design,  398,  400 
slip,  328,  339 

slots,  356,  386,  387,  389,  398 
voltage,  400,  411 
winding,  323,  327,  408 

Sandwiched  coils  for  transformers, 

434,  438,  484 
Saturation  curves,  no-load,  46,  240, 

342 

full-load,  59,  212,  227,  237,  309 
Screen  covered  motors,  135,  350,  383 


Segmental  punchings  for  armatures, 

22,  28,  192,  351 
Segments  of  commutator,  number, 

18,  138 

Selective  commutation,  19 
Self    induction    of    windings.     See 
Reactance  and  Reactance 
Voltage. 

Semi-enclosed  motors,  135,  350,  383 
Series  field  design,  68 
windings,  17,  21 

commutation  with,  19,  83 
Shafts,  278,  504 

Shell   type   transformers,    construc- 
tion, 436 
heating,  465 
insulation,  459 
procedure  in  design,  483 
reactance.  447,  485,  489 
three-phase,  491 
Short  circuit,  33 

sudden,  282,  314,  488 
test  on  alternators,  224 
on  induction  motors,  344 
on  transformers,  430,  495, 

496 
pitch  windings,  15,  82,  181,  189, 

419 

Silk  covering  for  wires,  31 
Simplex  windings,  7 
Single-phase   alternators,    armature 

reaction,  231 
turbos,  295 

windings,  160,  177,  188 
Singly  re-entrant  windings,  8 
Size  of  machine  and  frequency,  415, 

493 

and  output,  114,  255,  391 
and  regulation,  241 
Skew  coils,  176 
Slip,  328,  339 

rings,  194,  327 
Slots,  dimensions,  80,  123,  131,  146, 

256,  260,  262,  397,  398 
effect  on  wave  form,  180 
insulation,  36,  203,  411 
number,  22,  87,  180,  260,  396, 
398,  416 


526 


INDEX 


Slots,  open  and  closed,  24,  252,  349, 

356,  381,  411 
space  factor,  132 
Slow  speed  motors,  409 
Space  factor  in  slots,  132 
of  field  coils,  65,  243 
Speed  and  characteristics,  157,  316, 

392,  409,  426 

and  torque  curves,  328,  420 
frequency  and  poles,  162,  322 
limitations  in  design,  141,  272, 

417 
peripheral    of    armatures,    142, 

144 

of  commutators,  120 
of  rotors,  272,  275,  290,  416 
synchronous,  322 
Sparking,  cause,  75 
criteria,  75,  90 

prevention,  76,  85,  87,  90,  91 
voltage,  85 
Spiders,  350,.  500 
Specifications,  153,  312,  422,  494 
Starting  current,  325,  424 

torque,  and  rotor  loss,  325,  341 

372 

dead  points,  310,  388 
in  two  pole  motors,  418 
synchronous    horse-power, 

341,  345,  347 
sychronous  motors,  309 
Squirrel  cage  dampers,  295,  303 

rotors,    construction,   323,   350, 

422 

current  density,  380,  381 
flux  density,  358,  381 
heating  at  starting,  379 
losses,  355,  371 
procedure  in  design,  398 
Stator,  construction,  197,  348,  499 
current  density,  253,   262,   293, 

380 

flux  density,  252,  282,  358,  381 
generated  e.m.f.,  178,  352 
heating,  252,  281,  380 
insulation,  203 
losses,  247,  355,  371 
procedure  in  design,  255,  391 


Stator  reactance,  215,  233,  285,  360 
resistance,  248 
slots,   180,  256,  260,  262,  396, 

398,  416 
strength  relative  to  field,  229, 

290 

windings,  160,  322 
Steel.     See  Iron  and  Cast  Steel. 
Strength    of    main    and    armature 

fields,  61,  229,  290 
Surface  creepage,  34,  450,  454,  455, 

456 

Sub-synchronous  speed,  418 
Synchronous  motor  design,  308 
excitation,  306 
power  factor  correction  effect, 

306 

size,  307 
starting  torque,  309 

Tanks   for   transformers,    466,    482, 

486,  494 
Tape,  30 
Teeth,  dimensions,  80,  123,  131,  146, 

256,  260,  262,  397,  398 
effect  on  wave  form,  180 
flux  density,  45,  46,   107,  252, 

282,  358,  381 
Temperature  rise,  by  resistance,  63, 

465,  466 
guarantees,  133,  155,  314,  424, 

496 

maximum,  62,  104,  464,  473 
of  alternator  rotors,  239 

stators,  252 
of  commutators,  111 
of  d.-c.  armatures,  104 
of  enclosed  machines,  134,  382 
of  field  coils,  62,  239 
of  high  voltage  coils,  109,  250, 

253 

of  induction  motors,  375 
of  oil  in  bearings,  98,  314 
of  semi-enclosed  machines,  383 
of  transformers,  463 
of  turbos,  274,  279,  295,  315 
Tests  for  efficiency,   154,  313,  423, 
495 


INDEX 


527 


Tests  for  saturation,  342 
for  short  circuit,  344 
Theory  of  operation  of  alternator, 

208 

of  induction  motor,  319 
of  transformer,  427 
Thickness  of  core  laminations,  100, 

191,  348,  350,  440 
of  insulating  materials,  32,  201, 

461 

of  mica  in  commutators,  27 
of  slot  insulation,  39,  201,  203, 

205,  206 
Third  harmonic  and  connection  of 

winding,  183 
Three-finger  rule,  3 
Three-phase  power,  169 
transformers,  489 
windings,  162 

Torque  and  speed  curves,  328,  420 
in     synchronous     horse-power, 

341,  345,  347 
maximum,  328,  341,  347 
starting,    in   induction   motors, 

325,  341,  372,  388,  418 
in  synchronous  motors,  309 
Transformers,  construction,  433,  494 
current  density,  475 
excitation,  440,  481,  485 
flux  density,  479 
generated  e.m.f.,  439 
heating,  463 
insulation,  438,  449 
losses,  439,  461 
procedure  in  design,  476 
reactance,  445,  482 
theory  of  operation,  427 
vector  diagrams,  427 
Turbo  d.-c.  machines,  143 
Turbo  alternators,  construction,  275 
flux  densities,  282 
heating,  274,  279,  295 
procedure  in  design,  290 
reactance  of  armature,  285 
reactions  of  armature,  289 
shaft,  278 
single-phase,  295 
stresses,  275 


Two-phase  windings,  162 
Two-pole  motor,  418 

Unbalanced  magnetic  pull,  501 

Variable  speed  motor,  136,  426 

Varnish,  32,  450 

Vector  diagrams,  alternator,  210 

induction  motor,  329,  333 

transformer,  427 

Vent  ducts,  in  armature  and  stator 
cores,  24,  28,  192,  349 

in  field  coils,  40 

Ventilation  of  air  blast  transform- 
ers, 469 

of  commutators,  27,  111 

of  d.-c.  armatures,  24,  28,  109 

of  field  coils,  40 

of  induction  motors,  349,  382 

of  power  house,  252 

of  turbo  alternators,  281 
Vibration  and  insulation,  33 
Volt  ampere  rating,  188 
Voltage    and    characteristics,     156, 
315,  420,  424,  425,  496 

between  adjacent  commutator 
segments,  95,  138,  143 

limitations  in  design,  138,    294, 
488 

per  turn  in  transformers,  476 

Water  cooled  transformer,  470 

wheel  driven  alternators,   252, 

272 

Wave  form,  178,  315 
windings,  20,  170 
Windage,  98,  385 
Winding,   choice  of,   123,   127,   128, 

140,  260,  397 
for  different  voltages,  130,  267, 

407 

pitch,  15,  20 
Windings,  A.-C.,  chain,  169 

distributed,  171,  180,  187 

double  layer,  170 

odd  number  of  coil  groups, 

176 
several  circuits,  171 


528 


INDEX 


Windings,  A.   C.,  short  pitch,   181, 

189,  419 

single-phase,  160,  177,  188 
three-phase,  162 
two-phase,  162 
wave,  170 
Y  and     A-connected,    163, 

183,  407 

D.-C.,  compensating,  96 
dead  coils,  22,  130 
double  layer,  13 
doubly  re-entrant,  8 
drum,  9 
duplex,  8,  20 
equalizers,  13,  19,  22 
Gramme  ring,  7,  9 
lap,  20 

multiple,  16,  21,  79,  140 
progressive,  18 
re-entrant,  8 
retrogressive,  19 


Windings,  D.-C.,  series,  17, 19,  21,  83 
short  pitch,  15,  82 
simplex,  7 
wave,  20 
Wire  table,  508 

size  for  field  coils,  65 
size  for  transformer  coils,  475 
Wood,  450 
Wound  rotor    motor,    construction, 

327,  351 

procedure  in  design,  400 
rotor  voltage,  400,  411 
theory,  327 

Y-connection,  163,  260 

and  harmonics,  183 
Yoke  construction,  25,  29,  191,  350, 
499 

flux  density,  45,  67 

Zig  zag  leakage,  361,  387 


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Itfft 


NOV  .10 1941 M. 


AUG  37    1Q44 


JAN    111947 


DEC   4  1940M 

. 


LD  21-100m-7,'39(402s) 


TU 


995887 


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